Transformations

Problem 1

Find the reflection of the point $P=(-4,-1)$ across the x-axis. What are the new coordinates?

See Solution

Problem 2

Find the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

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Problem 3

Find the translation rule $\mathrm{T}(\mathrm{x}, \mathrm{y})=(\mathrm{x}-[?], \mathrm{y}+[\mathrm{]})$ for points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

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Problem 4

Find the new coordinates of $(-1,3)$ after moving 2 units down and rotating $270^{\circ}$ counterclockwise around the origin.

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Problem 5

Find the image of point $P=(2,-1)$ after a $270^{\circ}$ counterclockwise rotation about the origin. $(-1,[?])$

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Problem 6

If $P=(-2,7)$ , find the reflection of point $P$ across the y-axis.

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Problem 7

Find the image of point $P=(2,-1)$ after a $270^{\circ}$ counterclockwise rotation about the origin.

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Problem 8

What conjecture about the triangle's perimeter could Maryanne have made after the translation $(x-10, y+17)$ ?

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Problem 9

What could Maryanne's conjecture about the triangle's perimeter be after the translation $(x-5, y+11)$ ?

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Problem 10

Translate Triangle RST with vertices $R (-4,2)$ , $S (5,3)$ , $T (2,-5)$ , 4 down and 3 left. Find new coordinates.

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Problem 11

Check if triangles $\triangle ABC$ and $\triangle XYZ$ are congruent using transformations: reflect and translate.

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Problem 12

Find the line of reflection for triangle $XYZ$ with $Z'(10,8)$ given $X(4,-5)$ , $Y(6,-1)$ , $Z(10,-8)$ .

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Problem 13

Reflect point $C(-1,-6)$ across the line $y=4$ . What are the coordinates of $C^{\prime}$ ?

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Problem 14

Find the new vertices $K^{\prime}, L^{\prime}, M^{\prime}, N^{\prime}$ after rotating polygon KLMN by $90^{\circ}$ clockwise.

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Problem 15

What happens to a function's graph when multiplied by -1? A. Flips over $y=x$ . B. Flips over $y$ -axis. C. Flips over $x$ -axis.

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Problem 16

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

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Problem 17

Find the graph of $g(x)=\frac{1}{4} f(x)$ given $f(x)=x^{2}$ .

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Problem 18

Rotate the vector $(-5,3)$ using the matrix $\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$ . Find the terminal $x$ -value. $x=$

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Problem 19

Rotate the vector $\begin{bmatrix}-5 \\ -3\end{bmatrix}$ using the matrix $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$ . Find the $x$ -value of the new vector. $x=$

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Problem 20

Identify the transformation for $\triangle XYZ$ from $\triangle ABC$ and describe the rule for transforming $D(0,3)$ to $D'(3,0)$ .

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Problem 21

Find the vertices of parallelogram $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime} D^{\prime \prime}$ after dilation by 4 and reflection. Are the parallelograms similar or congruent?

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Problem 22

A triangle with vertices $A(0,0), B(2,0), C(0,4)$ is rotated $180^{\circ}$ and dilated by 3. Find new coordinates and similarity/congruence.

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Problem 23

Find the new coordinates of B (-5,-8), C (-5,-3), D (0,-3), E (0,-8) after a $180^{\circ}$ rotation around the origin.

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Problem 24

Find the new coordinates of vertices B $(2,-9)$ , C $(2,-4)$ , and D $(1,-9)$ after a $270^{\circ}$ clockwise rotation.

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Problem 25

Muna's gecko is $\frac{1}{2}$ inch wide and 5 inches long. If she makes it 1 inch wide, how long will the drawing be? Show your work.

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Problem 26

Reflect the square CDEF with vertices C(3,2), D(10,2), E(10,9), F(3,9) over the line $y=-x$ .

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Problem 27

Reflect points $A(2,1), B(6,1), C(4,3)$ across the line $y=-3$ .

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Problem 28

Find the new coordinates of points $A(-4,2)$ , $B(-7,-1)$ , and $C(0,1)$ after reflecting across the $x$ -axis.

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Problem 29

Translate $(x, y) \rightarrow(x-4, y+1)$ and reflect the result across the line $y=1$ .

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Problem 30

Find the equation of line $v$ that is perpendicular to $y=-\frac{9}{4} x+1$ and passes through the point $(-3,2)$ .

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Problem 31

Construct a figure where $\overline{XY}$ is perpendicular to $\overline{YZ}$ . What are the first and second steps?

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Problem 32

Sketch the graphs of $f(x)=x^{2}$ and $g(x)=\frac{1}{8} x^{2}$ . Find the points of $g(x)$ corresponding to $(-1,1),(0,0),(1,1)$ .

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Problem 33

Which option is not a similarity transformation: a. Translation, b. Dilation, c. Rotation, d. Stretch?

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Problem 34

A triangle transforms from $XY Z$ (perimeter 40) to $X'Y'Z'$ (perimeter 100). Find the transformation and $XY, Y'Z'$ . Options: a, b, c, d.

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Problem 35

Identify if the transformation $H(x, y) \rightarrow (2x, 5y)$ is a stretch or dilation.

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Problem 36

Determine if the transformation $L(x, y) \to (0.3x, 2y)$ is a stretch or dilation.

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Problem 37

Find the lengths after dilating points A and B from center O with a scale factor of 3: OA=3, OB=5, AB=4. OA'=?

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Problem 38

Is rotation a similarity transformation? Answer True or False.

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Problem 39

Dilation is a non-isometric transformation. True or False?

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Problem 40

Moises's original volume is 37500 cm³. If shrunk by a scale factor of $k=\frac{1}{4}$ , what is his new volume?

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Problem 41

Determine the transformations to show $\triangle QRS \cong \triangle TUV$ . Choose all correct options: A) Reflect across $x$ , then $y$ , then $x$ . B) Reflect across $y$ . C) Rotate $90^{\circ}$ clockwise, then reflect across $y$ . D) Rotate $180^{\circ}$ , then reflect across $x$ . E) Translate $4$ units left.

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Problem 42

Find the pre-image of vertex $A^{\prime}(8,5)$ after reflection across the $y$ -axis. Options: $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

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Problem 43

Figure $B$ is in Quadrant IV. After reflecting, rotating, and translating it, determine if these statements are true or false:
a. $B'''$ is in Quadrant II. b. $B$ is in Quadrant III. c. The $x$ -coordinates of $B'''$ are all negative. d. The $y$ -coordinates of $B''$ are all positive.
Initial position and shape of $B$ are needed.

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Problem 44

Find which reflection of the segment from $(-4,-6)$ to $(-6,4)$ gives endpoints $(4,-6)$ and $(6,4)$ .

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Problem 45

Combine the following translations into a single translation:
21. $T_{\langle-3,3\rangle} \circ T_{\langle-2,4\rangle}$
22. $T_{\langle-4,-3\rangle} \circ T_{\langle 3,1\rangle}$
23. $T_{\langle 5,-6\rangle} \circ T_{\langle-7,5\rangle}$
24. $T_{\langle 8,-2\rangle} \circ T_{\langle-4,9\rangle}$

See Solution

Problem 46

Find the reflection rule for triangle $C(3,8), D(5,12), E(4,6)$ to $C'(-8,-3), D'(-12,5), E'(-6,-4)$ .

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Problem 47

Triangle ABC with vertices A(4,2), B(2,7), C(6,5) is translated. Which transformations map it to A''B''C''? Options: A, B, or C?

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Problem 48

Travis has a 4" x 6" photo. a) If enlarged to 16" wide, what is the new height? b) Can it be enlarged to 8" x 10"? Answer y or $n$ .

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Problem 49

Reflect the point $P(-6,6)$ over the $y$ -axis. What are the coordinates of $P^{\prime}$ ?

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Problem 50

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

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Problem 51

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?

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Problem 52

Reflect the point $T(-3,2)$ over the $y$ -axis. What are the coordinates of $T^{\prime}$ ?

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Problem 53

What is the scale of Paco's drawing if the longest side is 5 inches and the original is 10 inches with a length of 4 in. : 5 yd?

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Problem 54

B) Une cuve a un observateur à $\mathrm{O}$ (1.20 m au-dessus de AB) et un poisson à $\mathrm{P}$ (0.80 m en dessous).
3) Quelle distance l'observateur pense-t-il voir le poisson ? Quelle distance le poisson voit-il l'observateur ?
4) Avec un miroir au fond (CD) et une épaisseur d'eau $\mathrm{e}=1.20 \mathrm{~m}$ , à quelle distance l'observateur voit-il son image ?
Comment cela change-t-il si l'eau s'écoule ?

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Problem 55

Explain the relationship between the graphs of $g(x) = x^{2} + 1$ and $f(x) = x^{2}$ .

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Problem 56

Find the new coordinates of point $N$ after dilating triangle $M N O$ by a factor of 3 from the origin, given $N(4,6)$ .

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Problem 57

Draw a line perpendicular to line $\ell$ at point $A$ . Identify line $\ell$ and point $A$ from the diagram.

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Problem 58

Translate the point (1,-6) by 2 units right and 6 units down. Show your work.

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Problem 59

Find the translation from point $Q(-9,-5)$ to $Q^{\prime}(-2,-8)$ as $\langle x, y \rangle$ .

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Problem 60

Find the translation from point $Q(-9,-5)$ to $Q^{\prime}(-2,-8)$ as $\langle x, y\rangle$ . Show your work.

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Problem 61

Find the translation from $Q(3,6)$ to $Q^{\prime}(9,3)$ as $\langle x, y\rangle$ . Show your work.

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Problem 62

Find the length of segment $\overline{A^{\prime} B^{\prime}}$ after dilating $\overline{AB}$ with A(1,15), B(10,3) by $\frac{2}{3}$ .

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Problem 63

Scale a polygon with sides 3, 1, 2, 1, and 2 units to a perimeter of 30 units. Find the scale factor and explain your reasoning.

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Problem 64

Translate the vertices A(2,-6), B(-1,-1), C(-3,-5) by $(x, y) \rightarrow (x+3, y+5)$ . Find A', B', C'.

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Problem 65

A translation moves point $V(-2,3)$ to $V^{\prime}(-2,7$ . Identify true statements about the translation.

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Problem 66

Find new coordinates of vertices $M'$ , $P'$ , $Q'$ , and $V'$ after a $270^{\circ}$ rotation of parallelogram $MPQV$ around $(-5,-10)$ .

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Problem 67

Identify the transformation rule for segments AB (A(1,-4), B(6,4)) and A'B' (A'(2,0), B'(6,0)). Choices are:
1. $(x, y) \longrightarrow(x+4, y+4)$
2. $(x, y) \longrightarrow(x, y+4)$
3. $(x, y) \longrightarrow(-x,-y)$
4. $(x, y) \longrightarrow(x, y-4)$

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Problem 68

Find the scale factor from segment EF (E(4,4), F(8,4)) to segment $E^{\prime} F^{\prime}$ (E'(-1,1), F'(2,1)). Options: $\frac{1}{3}$ , 3, $\frac{1}{4}$ , 4.

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Problem 69

Find the new vertices of $\triangle A B C$ after these translations: 1. $T_{\langle-2,3\rangle}$ , 2. $T_{\langle-4,-1\rangle}$ , 3. $T_{(4,6)}$ .

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Problem 70

Find the new coordinates of point $C'$ after rotating point $C(2, -3)$ 90 degrees clockwise and translating left by 2 units. Options: $(-1,2)$ , $(-5,2)$ , $(-6,-3)$ , $(-3,2)$ .

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Problem 71

Find the point on $g(t)$ if $(1,90)$ on $f(t)$ is translated 2 units right and reflected over the $x$ -axis.

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Problem 72

Find the reflection of the line $x=4$ across the $y$ -axis.

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Problem 73

Translate points D(-4,-5), E(0,-5), F(-1,-3), G(-3,-3) left 3 units and down 2 units. Find D', E', F', G'.

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Problem 74

Rotate points $U(-3,6)$ , $V(-8,1)$ , and $W(-3,1)$ by $180^{\circ}$ around the origin. Find $U^{\prime}, V^{\prime}, W^{\prime}$ .

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Problem 75

Describe the rotation that transforms triangle DEF with vertices $D(0,3), E(1,8), F(-3,4)$ to $D^{\prime}(3,0), E^{\prime}(8,-1), F(4,3)$ .

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Problem 76

Find the translation from triangle $K M N$ with vertices $K(12,3), M(-5,2), N(8,-4)$ to $K^{\prime}(18,0), M^{\prime}(1,-1), N^{\prime}(14,-7)$ .

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Problem 77

Find the translation from triangle $K M N$ with vertices $K(12,3), M(-5,2), N(8,-4)$ to $K^{\prime}(18,0), M^{\prime}(1,-1), N^{\prime}(14,-7)$ .

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Problem 78

Describe the rotation that transforms triangle $P Q R$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P^{\prime}(-9,2)$ , $Q^{\prime}(-1,0)$ , $R^{\prime}(7,-3)$ .

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Problem 79

Find the rotation that transforms triangle $PQR$ with vertices $P(9,-2)$ , $Q(1,0)$ , $R(-7,3)$ to $P'(-9,2)$ , $Q'(-1,0)$ , $R'(7,-3)$ .

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Problem 80

Reflect triangle $G H J$ with vertices $G(-5,3), H(2,6), J(-6,2)$ to get $G^{\prime}(5,3), H^{\prime}(-2,6), J^{\prime}(6,2)$ .

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Problem 81

Reflect triangle STW across the x-axis to get triangle S'T'W' with vertices $S'(15,6)$ , $T'(-2,-3)$ , $W'(-8,8)$ .

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Problem 82

Find the coordinates of $\mathrm{C}^{\prime}$ if point C is (0, -3) and transformed by $(x, y) \longrightarrow (y+4,-x)$ .

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Problem 83

Identify the graph of the function from reflecting $f(x)=\frac{1}{4}(8)^{x}$ across the y-axis and x-axis.

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Problem 84

Translate a figure 1 unit right and 3 units down. Plot the new points of the translated figure.

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Problem 85

Siva sees a scale drawing half the width and height of the original. Is the scale factor $\frac{1}{2}$ correct? Explain.

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Problem 86

Find the new coordinates of the point $(2,-6)$ after applying the transformations $R_{270^{\circ}}$ and then $r_{\mathrm{y} \text{-axis}}$ .

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Problem 87

Find the standard matrix for the linear transformation $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ that rotates points by $-\frac{5 \pi}{4}$ radians. $A=$

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Problem 88

Find the standard matrix for the linear transformation $T$ that rotates points in $\mathbb{R}^2$ by $-\frac{\pi}{2}$ radians. $A =$ (Enter exact values for each matrix element.)

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Problem 89

Rotate the points F(-5,-3), G(-6,-1), H(-1,-1), J(-2,-3) 3 degrees clockwise around the origin. Find new coordinates.

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Problem 90

Find the new coordinates of point $D'$ after dilating $D(-3,2)$ by a scale factor of $3$ from center $(0,0)$ .

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Problem 91

Find the new coordinates of point $C(-3,1)$ after translating the triangle 3 units left and 2 units up. Options: $(-2,-1)$ , $(-1,0)$ , $(3,0)$ , $(4,-1)$ .

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Problem 92

Find two transformations that map rectangle $ABCD$ to $A'B'C'D$ . Choose from: A, B, C, D, E.

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Problem 93

Triangle $PQR$ is dilated by a factor of 3. Which comparisons are correct for triangles $PQR$ and $P'Q'R'$ ? A. $\overline{P'R'}=\overline{PR}$ B. $\overline{P'R'}=3 \times \overline{PR}$ C. $\mathrm{m} \angle P'R'Q'=\mathrm{m} \angle PRQ$ D. $\mathrm{m} \angle P'R'Q'=3 \times \mathrm{m} \angle PRQ$

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Problem 94

A triangle at $(-2,-2),(-4,4),(2,2)$ is doubled in size. What are the new coordinates? Options: $(-4,-4),(-8,8),(4,4)$ or others.

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Problem 95

Identify the correct transformation from triangle $ABC$ (A(1,1), B(1,2), C(2,1)) to $A'B'C'$ (A'(3,3), B'(3,4), C'(4,3)). Options:
1. $f(x, y)=(x-2, y+2)$
2. $f(x, y)=(x+1, y+2)$
3. $f(x, y)=(3 x, 3 y)$
4. $f(x, y)=(x+2, y+2)$

See Solution

Problem 96

Find the rotation applied if the domain is $(-4,-2),(5,9),(-6,2)$ and the range is $(-2,4),(9,-5),(2,6)$ .

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Problem 97

Find the line of reflection for the points $(-4,1)$ and $(4,1)$ .

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Problem 98

Identify the transformation that moves square $E$ (diamond shape) to square $F$ after spinning it. Options: A. Translation B. Rotation C. Reflection

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Problem 99

Identify the transformation from $f(x)=x^{2}$ to $g(x)$ for $g(x)=(x-1)^{2}$ and $g(x)=(x+3)^{2}$ . Graph both.

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Problem 100

If segment $\overline{TU}$ is 26 units and dilated by $\frac{1}{4}$ , what is the length of $\overline{T^{\prime} U^{\prime}}$ ?

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Transformations

Problem 1

Find the reflection of the point P=(−4,−1)P=(-4,-1)P=(−4,−1) across the x-axis. What are the new coordinates?

Problem 2

Find the number that completes the translation rule T(x,y)=(x−5,y+[?])T(x, y)=(x-5, y+[?])T(x,y)=(x−5,y+[?]) given points P(7,5)\mathrm{P}(7,5)P(7,5) and P′(2,8)\mathrm{P}^{\prime}(2,8)P′(2,8).

Problem 3

Find the translation rule T(x,y)=(x−[?],y+[])\mathrm{T}(\mathrm{x}, \mathrm{y})=(\mathrm{x}-[?], \mathrm{y}+[\mathrm{]})T(x,y)=(x−[?],y+[]) for points P(7,5)\mathrm{P}(7,5)P(7,5) and P′(2,8)\mathrm{P}^{\prime}(2,8)P′(2,8).

Problem 4

Find the new coordinates of (−1,3)(-1,3)(−1,3) after moving 2 units down and rotating 270∘270^{\circ}270∘ counterclockwise around the origin.

Problem 5

Find the image of point P=(2,−1)P=(2,-1)P=(2,−1) after a 270∘270^{\circ}270∘ counterclockwise rotation about the origin. (−1,[?])(-1,[?])(−1,[?])

Problem 6

If P=(−2,7)P=(-2,7)P=(−2,7), find the reflection of point PPP across the y-axis.

Problem 7

Find the image of point P=(2,−1)P=(2,-1)P=(2,−1) after a 270∘270^{\circ}270∘ counterclockwise rotation about the origin.

Problem 8

What conjecture about the triangle's perimeter could Maryanne have made after the translation (x−10,y+17)(x-10, y+17)(x−10,y+17)?

Problem 9

What could Maryanne's conjecture about the triangle's perimeter be after the translation (x−5,y+11)(x-5, y+11)(x−5,y+11)?

Problem 10

Translate Triangle RST with vertices R(−4,2)R (-4,2)R(−4,2), S(5,3)S (5,3)S(5,3), T(2,−5)T (2,-5)T(2,−5), 4 down and 3 left. Find new coordinates.

Problem 11

Check if triangles △ABC\triangle ABC△ABC and △XYZ\triangle XYZ△XYZ are congruent using transformations: reflect and translate.

Problem 12

Find the line of reflection for triangle XYZXYZXYZ with Z′(10,8)Z'(10,8)Z′(10,8) given X(4,−5)X(4,-5)X(4,−5), Y(6,−1)Y(6,-1)Y(6,−1), Z(10,−8)Z(10,-8)Z(10,−8).

Problem 13

Reflect point C(−1,−6)C(-1,-6)C(−1,−6) across the line y=4y=4y=4. What are the coordinates of C′C^{\prime}C′?

Problem 14

Find the new vertices K′,L′,M′,N′K^{\prime}, L^{\prime}, M^{\prime}, N^{\prime}K′,L′,M′,N′ after rotating polygon KLMN by 90∘90^{\circ}90∘ clockwise.

Problem 15

What happens to a function's graph when multiplied by -1? A. Flips over y=xy=xy=x. B. Flips over yyy-axis. C. Flips over xxx-axis.

Problem 16

Compare the graphs of f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=4x2g(x)=4x^{2}g(x)=4x2. Which statement is true about their relationship?

Problem 17

Find the graph of g(x)=14f(x)g(x)=\frac{1}{4} f(x)g(x)=41​f(x) given f(x)=x2f(x)=x^{2}f(x)=x2.

Problem 18

Rotate the vector (−5,3)(-5,3)(−5,3) using the matrix [01−10]\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right][0−1​10​]. Find the terminal xxx-value. x= x= x=

Problem 19

Rotate the vector [−5−3]\begin{bmatrix}-5 \\ -3\end{bmatrix}[−5−3​] using the matrix [01−10]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[0−1​10​]. Find the xxx-value of the new vector. x= x= x=

Problem 20

Identify the transformation for △XYZ\triangle XYZ△XYZ from △ABC\triangle ABC△ABC and describe the rule for transforming D(0,3)D(0,3)D(0,3) to D′(3,0)D'(3,0)D′(3,0).

Problem 21

Find the vertices of parallelogram A′′B′′C′′D′′A^{\prime \prime} B^{\prime \prime} C^{\prime \prime} D^{\prime \prime}A′′B′′C′′D′′ after dilation by 4 and reflection. Are the parallelograms similar or congruent?

Problem 22

A triangle with vertices A(0,0),B(2,0),C(0,4)A(0,0), B(2,0), C(0,4)A(0,0),B(2,0),C(0,4) is rotated 180∘180^{\circ}180∘ and dilated by 3. Find new coordinates and similarity/congruence.

Problem 23

Find the new coordinates of B (-5,-8), C (-5,-3), D (0,-3), E (0,-8) after a 180∘180^{\circ}180∘ rotation around the origin.

Problem 24

Find the new coordinates of vertices B (2,−9)(2,-9)(2,−9), C (2,−4)(2,-4)(2,−4), and D (1,−9)(1,-9)(1,−9) after a 270∘270^{\circ}270∘ clockwise rotation.

Problem 25

Muna's gecko is 12\frac{1}{2}21​ inch wide and 5 inches long. If she makes it 1 inch wide, how long will the drawing be? Show your work.

Problem 26

Reflect the square CDEF with vertices C(3,2), D(10,2), E(10,9), F(3,9) over the line y=−xy=-xy=−x.

Problem 27

Reflect points A(2,1),B(6,1),C(4,3)A(2,1), B(6,1), C(4,3)A(2,1),B(6,1),C(4,3) across the line y=−3y=-3y=−3.

Problem 28

Find the new coordinates of points A(−4,2)A(-4,2)A(−4,2), B(−7,−1)B(-7,-1)B(−7,−1), and C(0,1)C(0,1)C(0,1) after reflecting across the xxx-axis.

Problem 29

Translate (x,y)→(x−4,y+1)(x, y) \rightarrow(x-4, y+1)(x,y)→(x−4,y+1) and reflect the result across the line y=1y=1y=1.

Problem 30

Find the equation of line vvv that is perpendicular to y=−94x+1y=-\frac{9}{4} x+1y=−49​x+1 and passes through the point (−3,2)(-3,2)(−3,2).

Problem 31

Construct a figure where XY‾\overline{XY}XY is perpendicular to YZ‾\overline{YZ}YZ. What are the first and second steps?

Problem 32

Sketch the graphs of f(x)=x2f(x)=x^{2}f(x)=x2 and g(x)=18x2g(x)=\frac{1}{8} x^{2}g(x)=81​x2. Find the points of g(x)g(x)g(x) corresponding to (−1,1),(0,0),(1,1)(-1,1),(0,0),(1,1)(−1,1),(0,0),(1,1).

Problem 33

Which option is not a similarity transformation: a. Translation, b. Dilation, c. Rotation, d. Stretch?

Problem 34

A triangle transforms from XYZXY ZXYZ (perimeter 40) to X′Y′Z′X'Y'Z'X′Y′Z′ (perimeter 100). Find the transformation and XY,Y′Z′XY, Y'Z'XY,Y′Z′. Options: a, b, c, d.

Problem 35

Identify if the transformation H(x,y)→(2x,5y)H(x, y) \rightarrow (2x, 5y)H(x,y)→(2x,5y) is a stretch or dilation.

Problem 36

Determine if the transformation L(x,y)→(0.3x,2y)L(x, y) \to (0.3x, 2y)L(x,y)→(0.3x,2y) is a stretch or dilation.

Problem 37

Find the lengths after dilating points A and B from center O with a scale factor of 3: OA=3, OB=5, AB=4. OA'=?

Problem 38

Is rotation a similarity transformation? Answer True or False.

Problem 39

Dilation is a non-isometric transformation. True or False?

Problem 40

Find the reflection of the point $P=(-4,-1)$ across the x-axis. What are the new coordinates?

Find the number that completes the translation rule $T(x, y)=(x-5, y+[?])$ given points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

Find the translation rule $\mathrm{T}(\mathrm{x}, \mathrm{y})=(\mathrm{x}-[?], \mathrm{y}+[\mathrm{]})$ for points $\mathrm{P}(7,5)$ and $\mathrm{P}^{\prime}(2,8)$ .

Find the new coordinates of $(-1,3)$ after moving 2 units down and rotating $270^{\circ}$ counterclockwise around the origin.

Find the image of point $P=(2,-1)$ after a $270^{\circ}$ counterclockwise rotation about the origin. $(-1,[?])$

If $P=(-2,7)$ , find the reflection of point $P$ across the y-axis.

Find the image of point $P=(2,-1)$ after a $270^{\circ}$ counterclockwise rotation about the origin.

What conjecture about the triangle's perimeter could Maryanne have made after the translation $(x-10, y+17)$ ?

What could Maryanne's conjecture about the triangle's perimeter be after the translation $(x-5, y+11)$ ?

Translate Triangle RST with vertices $R (-4,2)$ , $S (5,3)$ , $T (2,-5)$ , 4 down and 3 left. Find new coordinates.

Check if triangles $\triangle ABC$ and $\triangle XYZ$ are congruent using transformations: reflect and translate.

Find the line of reflection for triangle $XYZ$ with $Z'(10,8)$ given $X(4,-5)$ , $Y(6,-1)$ , $Z(10,-8)$ .

Reflect point $C(-1,-6)$ across the line $y=4$ . What are the coordinates of $C^{\prime}$ ?

Find the new vertices $K^{\prime}, L^{\prime}, M^{\prime}, N^{\prime}$ after rotating polygon KLMN by $90^{\circ}$ clockwise.

What happens to a function's graph when multiplied by -1? A. Flips over $y=x$ . B. Flips over $y$ -axis. C. Flips over $x$ -axis.

Compare the graphs of $f(x)=x^{2}$ and $g(x)=4x^{2}$ . Which statement is true about their relationship?

Find the graph of $g(x)=\frac{1}{4} f(x)$ given $f(x)=x^{2}$ .

Rotate the vector $(-5,3)$ using the matrix $\left[\begin{array}{cc}0 & 1 \\ -1 & 0\end{array}\right]$ . Find the terminal $x$ -value. $x=$

Rotate the vector $\begin{bmatrix}-5 \\ -3\end{bmatrix}$ using the matrix $\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}$ . Find the $x$ -value of the new vector. $x=$

Identify the transformation for $\triangle XYZ$ from $\triangle ABC$ and describe the rule for transforming $D(0,3)$ to $D'(3,0)$ .

Find the vertices of parallelogram $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime} D^{\prime \prime}$ after dilation by 4 and reflection. Are the parallelograms similar or congruent?

A triangle with vertices $A(0,0), B(2,0), C(0,4)$ is rotated $180^{\circ}$ and dilated by 3. Find new coordinates and similarity/congruence.

Find the new coordinates of B (-5,-8), C (-5,-3), D (0,-3), E (0,-8) after a $180^{\circ}$ rotation around the origin.

Find the new coordinates of vertices B $(2,-9)$ , C $(2,-4)$ , and D $(1,-9)$ after a $270^{\circ}$ clockwise rotation.

Muna's gecko is $\frac{1}{2}$ inch wide and 5 inches long. If she makes it 1 inch wide, how long will the drawing be? Show your work.

Reflect the square CDEF with vertices C(3,2), D(10,2), E(10,9), F(3,9) over the line $y=-x$ .

Reflect points $A(2,1), B(6,1), C(4,3)$ across the line $y=-3$ .

Find the new coordinates of points $A(-4,2)$ , $B(-7,-1)$ , and $C(0,1)$ after reflecting across the $x$ -axis.

Translate $(x, y) \rightarrow(x-4, y+1)$ and reflect the result across the line $y=1$ .

Find the equation of line $v$ that is perpendicular to $y=-\frac{9}{4} x+1$ and passes through the point $(-3,2)$ .

Construct a figure where $\overline{XY}$ is perpendicular to $\overline{YZ}$ . What are the first and second steps?

Sketch the graphs of $f(x)=x^{2}$ and $g(x)=\frac{1}{8} x^{2}$ . Find the points of $g(x)$ corresponding to $(-1,1),(0,0),(1,1)$ .

A triangle transforms from $XY Z$ (perimeter 40) to $X'Y'Z'$ (perimeter 100). Find the transformation and $XY, Y'Z'$ . Options: a, b, c, d.

Identify if the transformation $H(x, y) \rightarrow (2x, 5y)$ is a stretch or dilation.

Determine if the transformation $L(x, y) \to (0.3x, 2y)$ is a stretch or dilation.

Moises's original volume is 37500 cm³. If shrunk by a scale factor of $k=\frac{1}{4}$ , what is his new volume?

Find the pre-image of vertex $A^{\prime}(8,5)$ after reflection across the $y$ -axis. Options: $(-8,-6)$ , $(-6,8)$ , $(8,6)$ , $(6,-8)$ .

Find which reflection of the segment from $(-4,-6)$ to $(-6,4)$ gives endpoints $(4,-6)$ and $(6,4)$ .

Find the reflection rule for triangle $C(3,8), D(5,12), E(4,6)$ to $C'(-8,-3), D'(-12,5), E'(-6,-4)$ .

Travis has a 4" x 6" photo. a) If enlarged to 16" wide, what is the new height? b) Can it be enlarged to 8" x 10"? Answer y or $n$ .

Reflect the point $P(-6,6)$ over the $y$ -axis. What are the coordinates of $P^{\prime}$ ?

Graph the reflection of the point $T(10,-2)$ over the $x$ -axis.

Reflect the point $S(0,2)$ over the $x$ -axis. What are the coordinates of $S^{\prime}$ ?

Reflect the point $T(-3,2)$ over the $y$ -axis. What are the coordinates of $T^{\prime}$ ?

Explain the relationship between the graphs of $g(x) = x^{2} + 1$ and $f(x) = x^{2}$ .

Find the new coordinates of point $N$ after dilating triangle $M N O$ by a factor of 3 from the origin, given $N(4,6)$ .

Draw a line perpendicular to line $\ell$ at point $A$ . Identify line $\ell$ and point $A$ from the diagram.

Find the translation from point $Q(-9,-5)$ to $Q^{\prime}(-2,-8)$ as $\langle x, y \rangle$ .

Find the translation from point $Q(-9,-5)$ to $Q^{\prime}(-2,-8)$ as $\langle x, y\rangle$ . Show your work.

Find the translation from $Q(3,6)$ to $Q^{\prime}(9,3)$ as $\langle x, y\rangle$ . Show your work.

Find the length of segment $\overline{A^{\prime} B^{\prime}}$ after dilating $\overline{AB}$ with A(1,15), B(10,3) by $\frac{2}{3}$ .

Translate the vertices A(2,-6), B(-1,-1), C(-3,-5) by $(x, y) \rightarrow (x+3, y+5)$ . Find A', B', C'.

A translation moves point $V(-2,3)$ to $V^{\prime}(-2,7$ . Identify true statements about the translation.

Find new coordinates of vertices $M'$ , $P'$ , $Q'$ , and $V'$ after a $270^{\circ}$ rotation of parallelogram $MPQV$ around $(-5,-10)$ .

Find the scale factor from segment EF (E(4,4), F(8,4)) to segment $E^{\prime} F^{\prime}$ (E'(-1,1), F'(2,1)). Options: $\frac{1}{3}$ , 3, $\frac{1}{4}$ , 4.

Find the new vertices of $\triangle A B C$ after these translations: 1. $T_{\langle-2,3\rangle}$ , 2. $T_{\langle-4,-1\rangle}$ , 3. $T_{(4,6)}$ .

Find the new coordinates of point $C'$ after rotating point $C(2, -3)$ 90 degrees clockwise and translating left by 2 units. Options: $(-1,2)$ , $(-5,2)$ , $(-6,-3)$ , $(-3,2)$ .

Find the point on $g(t)$ if $(1,90)$ on $f(t)$ is translated 2 units right and reflected over the $x$ -axis.

Find the reflection of the line $x=4$ across the $y$ -axis.

Rotate points $U(-3,6)$ , $V(-8,1)$ , and $W(-3,1)$ by $180^{\circ}$ around the origin. Find $U^{\prime}, V^{\prime}, W^{\prime}$ .