Geometric transformations

What are the coordinates of the image of vertex R after a reflection across the y-axis?

(3, 4)

The rule ry-axis • RO, 90°(x, y) is applied to ΔABC. Which triangle shows the final image?

1

A point has the coordinates (0, k). Which reflection of the point will produce an image at the same coordinates, (0, k)?

not a not c

Which point would map onto itself after a reflection across the line y = -x?

(-4, 0)

Parallelogram ABCD is rotated to create image A'B'C'D'. Which rule describes the transformation?

(x, y) → (y, -x)

What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the y-axis?

(-6, 8)

Rectangle EFGH is translated according to the rule T-5, 9(x, y). If the coordinates of the pre-image of point H are (-2, -3), what are the coordinates of H'?

(-7, 6)

A composition of transformations maps ΔXYZ to ΔX"Y"Z". The first transformation for this composition is____________ , and the second transformation is a 90° rotation about point X'.

a reflection across line m

Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"?

not a

Rectangle A'B'C'D' is the image of rectangle ABCD after it has been translated according to the rule T-4, 3(x, y). Which points are vertices of the pre-image, rectangle ABCD? Check all that apply.

(-1, -2) (7, 1) (-1, 1) (7, -2)

A triangle has vertices at R(1, 1), S(-2, -4), and T(-3, -3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?

(-4, 2)

Which shows the image of ΔRST after the rotation (x, y) → (y, -x)?

a

Square A"B"C"D" is the final image after the rule T-4, -1 • RO, 90°(x, y) was applied to square ABCD. What are the coordinates of vertex A of square ABCD?

not b

A triangle is rotated 90° about the origin. Which rule describes the transformation?

not d

If the smallest angle of rotation for a regular polygon is 18°, how many sides does polygon have?

not d

Which figure has the same order of rotational symmetry as a rectangle?

rhombus

Which rule describes the composition of transformations that maps figure PQRS to figure P"Q'R"S"?

rl • RQ, 180°

What is the rule for the reflection?

rx-axis(x, y) → (x, -y)

The image of ΔABC after a reflection across is ΔA'B'C'. Which triangle must be a right triangle and why?

ΔBGC is right because CC'.

A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?

(x, y) → (x - 3, y + 5)

The image of parallelogram PQRS after a reflection across is parallelogram P'Q'R'S'. If RR' = 12, then RZ =

6

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.

Triangle XYZ is rotated to create the image triangle X'Y'Z'. Which rules could describe the rotation? Check all that apply.

R0, 180° (x, y) → (-y, x) (x, y) → (-x, -y)

Triangle QRS is transformed as shown on the graph. Which rule describes the transformation?

R0, 270°

One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0). Which transformations could have taken place? Check all that apply.

R0, 270° R0, -90°

Square PQRS is transformed as shown on the graph. Which rule describes the transformation?

R0, 90°

Irina wants to tile her floor using the translation shown below. Which is the rule for this translation?

T-3, 2(x, y)

Which rule represents the translation from the pre-image, ABCD, to the image, A'B'C'D'?

T2, 1(x, y)

If a quadrilateral has exactly 2 lines of symmetry, and both are angle bisectors, then which statement would be true?

The figure must be a rhombus because it has exactly 2 pairs of congruent angles.

Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?

a

Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

a

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)

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(-1, 2). The image of triangle XYZ after a rotation has vertices X'(-3, 1), Y'(0, 0), and Z'(-2, -1). Which rule describes the transformation?

R0, 90°

One vertex of a polygon is located at (3, -2). After a rotation, the vertex is located at (2, 3). Which transformations could have taken place? Check all that apply.

R0, 90° R0, -270°

The image of trapezoid PQRS after a reflection across is trapezoid P'Q'R'S'. What is the relationship between RR' and SS'?

RR' || SS'

Which triangle has 0 reflectional symmetries?

a

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.

a b c d

The rule as a mapping for the translation of a rectangle is (x, y) → (x - 2, y + 7). Which describes this translation?

a translation of 2 units to the left and 7 units up

Which figure shows a line of reflectional symmetry for the letter T?

c

Quadrilateral ABCD is transformed according to the rule (x, y) → (y, -x). Which is another way to state the transformation?

not a

The rule T5, -0.5 • RO, 180°(x, y) is applied to ΔFGH to produce ΔF"G"H". What are the coordinates of vertex F" of ΔF"G"H"?

(4, -1.5)

Triangle RST was transformed using the rule (x, y) → (-x, -y). The vertices of the triangles are shown. R (1, 1) R' (-1, -1) S (3, 1) S' (-3, -1) T (1, 6) T' (-1, -6) Which best describes the transformation?

The transformation was a 180° rotation about the origin.

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'

Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y - 3.5) to create the image ΔA'B'C' shown on the coordinate plane. Which graph shows the pre-image, ΔABC?

d

Which figure has an order 3 rotational symmetry?

equilateral triangle

Which figure represents the image of trapezoid LMNP after a reflection across the x-axis?

figure A

A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The triangle is transformed according to the rule R0, 180°. Which statements are true regarding the transformation? Check all that apply.

The rule for the transformation is (x, y) → (-x, -y). The coordinates of L' are (-2,-2). The coordinates of N' are (-1,-6).

Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Check all that apply.

The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2). The transformation is rigid. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2. If figure 1 is rotated 360° about point C, it will be mapped onto itself

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

Triangle XYZ with vertices X(0, 0), Y(0, -2), and Z(-2, -2) is rotated to create the image triangle X'(0, 0), Y'(2, 0), and Z'(2, -2). Which rules could describe the rotation? Check all that apply.

a R0, 90° d (x, y) → (-y, x)

Which composition of transformations maps figure EFGH to figure E"F"G"H"?

a reflection across line k followed by a translation down

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 letter in the word HAPPY has an order 2 rotational symmetry?

h

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?

not a

Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are (-9, 2), what are the coordinates of F'?

not a

Figure ABCD was reflected across the x-axis to create figure A'B'C'D'. What are the coordinates of the pre-image of B'?

(-8, -2)

Figure ABCDEF was reflected across the line y = -x to create figure A'B'C'D'E'F'. What are the coordinates of the pre-image of F'?

(2, -4)

Triangle JKL is transformed using the rule RO, 90° • ry = -x(x, y). Point K of the pre-image is at (4, 7). What are the coordinates of point K" on the final image?

(4, -7)

What are the coordinates of the image of vertex D after a reflection across the x-axis?

(5, 3)

Triangle ABC is translated according to the rule (x, y) → (x + 2, y - 8). If the coordinates of the pre-image of point B are (4, -5), what are the coordinates of B'?

(6, -13)

A triangle on a coordinate plane is translated according to the rule T-3, 5(x, y). Which is another way to write this rule?

(x, y) → (x - 3, y + 5)

A regular decagon has 10 sides. How many reflectional symmetries does a regular decagon have?

10

What is the order of rotational symmetry for a rhombus?

2

How many lines of reflectional symmetry does an equilateral triangle have?

3

Which angle of rotation is an angle of rotational symmetry for all figures?

360°

A point has the coordinates (m, 0) and m ≠ 0. Which reflection of the point will produce an image located at (0, -m)?

A point has the coordinates (m, 0) and m ≠ 0. Which reflection of the point will produce an image located at (0, -m)?

ΔA'B'C' was constructed using ΔABC and line segment EH. For the transformation to be a reflection, which statements must be true? Check all that apply.

BD = DB' CG = GC' m∠EFA = 90° The line of reflection, EH, is the perpendicular bisector of BB', AA', and CC'.

Quinton tried to transform triangle FGH according to the rule (x, y) → (-y, x). Which best describes his attempt?

Correct. He transformed the triangle according to the rule (x, y) → (-y, x).

Which statements are true about trapezoid ABCD and its translated image, A'B'C'D'? Check all that apply.

The rule for the translation can be written as T-3, 1(x, y). The rule for the translation can be written as (x, y) → (x - 3, y + 1).

A triangle has vertices at R(1, 1), S(-2, -4), and T(-3, -3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?

not c

If a translation of T2, -7(x, y) is applied to ΔABC, what are the coordinates of B'?

not c

Which point would map onto itself after a reflection across the line y = -x?

not c

Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?

not c