EMI1 Transformations
Which rotation maps point K(8, -6) to K'(-6, -8)?
90° clockwise rotation
Cedric applied the rule rm • RP, 90°(x, y) to figure WXYZ. What mistakes did he make? Check all that apply.
He applied the reflection to the pre-image first. He used an incorrect angle of rotation around point P.
Gregory knows that ABC is reflected onto A'B'C'. Which statement about the figures is true?
If Gregory draws the segment with endpoints A and A', then the midpoint will lie on the line of reflection.
Which composition of transformations maps figure EFGH to figure E"F"G"H"?
a reflection across line k followed by a translation down
Point G is rotated 90°. The coordinate of the pre-image point G was (7, -5), and its image G' is at the coordinate (5, 7). What is the direction of the rotation?
counterclockwise
Which rule describes the composition of transformations that maps figure PQRS to figure P"Q'R"S"?
rl • RQ, 180°
Triangle LMN is reflected across a line, L = (12, -7), and L' = (-7, 12). What is the line of reflection?
the line y = x
Triangle PQR is reflected across a line, P = (4,-5), and P' = (-4, -5). What is the line of reflection?
the y-axis
Which triangle is a translation of triangle P? mc005-1.jpg
triangle C
Which red triangle shows a 90° counterclockwise rotation of the blue triangle? Check all that apply.
A (mr022-1.jpg) B (mr022-2.jpg) F(mr022-5.jpg)
The triangles on the grid below represent a translation. mc004-1.jpg To form the image, the pre-image moved
five units right and three units up.
A translation is shown on the grid below in which triangle A is the pre-image and triangle B is the image. mc016-1.jpg Which rule describes the x-coordinates in the translation?
x + 6
The rule ry-axis • RO, 90°(x, y) is applied to ΔABC. Which triangle shows the final image?
1
Which triangle is a translation of triangle X? mc003-1.jpg
Triangle B
What is the equation for the line of reflection? mc019-1.jpg
y=x
After Hillary realized her clock was running 30 minutes fast, she used a knob on the clock to turn the minute hand back 30 minutes. Which describes the rotation of the minute hand?
NOT 90° counterclockwise rotation
Which graph shows a method for finding the image of point D if the parallelogram is reflected across the dashed line? mc015-1.jpg
NOT D
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?
T -6, -2 ° r x-axis(x, y) (answer A)
A translation moves point V(-2, 3) to V'(-2,7). Which are true statements about the translation?
The transformation rule is (x,y) -> (x+0,y+4). The transformation is a vertical translation.
Which rule describes the x-coordinates in the translation below?. mc015-1.jpg
x + 0
Which choice shows the coordinates of C' if the trapezoid is reflected across the y-axis? mc009-1.jpg
(-5, 3)
Triangle XYZ is rotated 90° counterclockwise about the origin. mc007-1.jpg What are the coordinates of point Y'?
(1, 4)
What are the coordinates of D' when the quadrilateral is reflected across the line y=x? mc010-2.jpg
(1,3)
Figure WXYZ is transformed using the rule ry-axis • T-4, 2(x, y). Point W of the pre-image is at (1, 6). What are the coordinates of point W" on the final image?
(3, 8)
Point A(7, 3) is translated to A'(16,-9). Which rule describes the translation?
(x,y) -> (x+9,y-12)
Which rule describes the translation below? mc018-1.jpg
(x,y) -> (x-5,y-3)
A rotation maps point A to A'. mc014-1.jpg Which statement describes the rotation?
180° rotation
Andrew's rotation maps point M(9, -1) to M'(-9, 1). Which describes the rotation?
180° rotation
Angie's rotation maps triangle XYZ to triangle X'Y'Z'. X(3, -6) maps to X'(-3, 6) Y(1, -2) maps to Y'(-1, 2) Z(-1, -5) maps to Z'(1, 5) Which describes the rotation?
180° rotation
Mira uses the mapping rule to find the coordinate of a point that had been rotated 90° clockwise about the origin. Examine Mira's solution to determine which step has an error. M(-5, -6) is rotated 90° clockwise. Step 1. Use the rule (x, y)g(y, -x). Step 2. Switch x and y coordinates: (-6, -5) Step 3. Multiply the new x-coordinate by -1: ((-1)-6, -5) Step 4. Simplify: (6, -5) Mira made an error in Step __.
3
A composition of transformations maps ΔKLM to ΔK"L"M". The first transformation for this composition is , and the second transformation is a translation down and to the right.
A 270 rotation about point P
Arionna needed to graph triangle PQR reflected across the y-axis. Her work is shown below. Arionna's Work: Blue -> Red P(3,7) -> P'(3,-7) Q(0,4) -> Q'(0,4) R(5,8) -> R'(-5,8) Arionna's Graph mr024-2.jpg
Arionna did not find the correct point for P'. She should have negated the x-value, not the y-value. Arionna switched the order of the coordinates of P' (3, -7) when she graphed them.
The triangle on the grid will be translated two units left. mc008-1.jpg Which shows the triangle when it is translated two units left?
B
Kadesha says that the triangles represent a translation. mc006-1.jpg Which explains whether Kadesha is correct?
Kadesha is not correct because the number of units between points A and B is different than those between points A' and B'.
What are the coordinates of A' after reflecting across the line x = 3? mc014-1.jpg
NOT (3,4)
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
NOT Point B is the result of a 90° counterclockwise rotation.
Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"?
NOT r x-axis ° T -6, 1 (x, y)
Triangle PQR has coordinates P(-8, 3), Q(-8, 6), and R(-3, 6). If the triangle is translated by using the rule (x,y) -> (x+4,y-6), what are the coordinates of triangle P'Q'R'?
P'(-4,-3),Q'(-4,0),R'(1,0)
Which statement about the reflection below is true? mc017-1.jpg
The distance between C and P is equal to the distance between C' and P.
Which choices correctly describe reflections in the diagram? Check all that apply. mr022-1.jpg
The red triangle A is reflected across the y-axis onto triangle D. The blue triangle D is reflected across the x-axis onto triangle C. The blue triangle D is reflected across the line y = x onto triangle B.
What is the final transformation in the composition of transformations that maps pre-image GHJK to image G'H"J"K"?
a reflection across line m
Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?
a reflection across line n followed by a 270° rotation about point P
Which image is a reflection of the black polygon in quadrant I? mc001-1.jpg
the red polygon in quadrant II
Rectangle PQRS is rotated 90° counterclockwise about the origin. mc004-1.jpg What are the coordinates of point Q'?
Q'( -3, 5)
Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?
T -2, 0 ° Ro, 90° (x, y) (answer D)
Which triangle on the coordinate grid is a translation of triangle F? es026-1.jpg
Triangle G
Iliana rotated trapezoid WXYZ 180° about the origin. mc011-1.jpg What is the correct set of image points for trapezoid W'X'Y'Z'?
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"?
a 270° rotation about point B'
Ryan wants to describe the translation shown on the grid below. mc007-1.jpg Ryan uses the following steps to describe the translation. Step 1 Identify the pre-image and the image: The pre-image is triangle XYZ, and the image is mc007-2.jpg. Step 2 Identify the number of units that each point moves horizontally: Each point moves one unit left. Step 3 Identify the number of units that each point moves vertically: Each point moves three units down. Step 4 The translation is one unit left and three units down. In which step did Ryan make the first error?
Step 3
Point A has coordinate A(3, 2). The point is rotated 180° clockwise about the origin. What is the x-coordinate of point A'?
NOT (-3,-2)
The rule ry = x • T4, 0(x, y) is applied to trapezoid ABCD to produce the final image A"B"C"D". Which ordered pairs name the coordinates of vertices of the pre-image, trapezoid ABCD? Check all that apply.
(-1, 0) (-1, -5) (1, -1) (1, -4)
Parallelogram F"G"H"J" is the final image after the rule ry-axis • T1,2(x, y) was applied to parallelogram FGHJ. What are the coordinates of vertex F of parallelogram FGHJ?
(-4, 2)
A translation is shown on the grid below. mr023-1.jpg Which are true statements about the translation?
The sides of the image and pre-image are congruent. The image is a slide of the pre-image. Each point has moved the same number of units.