Geometric transformations Section 4 Honors Geometry

Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y - 3.5) to create the image ΔA'B'C' if A is (2, 1) what are the coordinates of A'?

A' (3.5, -2.5)

If a translation of T2, -7(x, y) is applied to ΔABC, what are the coordinates of B'? B(1,10)

B'(3,3)

Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"? J(2,3) J'(1,1.5)J''(1.5,1)

Dilation by a factor of 1/2, reflected over y=x

Cedric applied the rule R90°(x, y) to figure WXYZ. W(2,1)W'(1-2) X(3,7) X'(7,-3) Y(-2,4) Y' (4,2) Z(-1,-2) Z'(-2,1) What mistake did he make?

He rotated 90 degrees clockwise instead of counter clockwise

Triangle QRS is transformed as shown on the graph. Q(-2,5) Q'(5,2) Which rule describes the transformation?

R0, 270°

Square PQRS is transformed as shown on the graph. P(3,1) P'(-1,3) Which rule describes the transformation?

R0, 90°

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 rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"? If A is (2,3) and A'' (-6,-4)

Reflected across line y=-x and dilated with a scale factor of 2

Irina wants to tile her floor using the translation shown below. Which is the rule for this translation? A(2,4) A'(-1,6)

T-3, 2(x, y)

Which rule represents the translation from the pre-image, ABCD, to the image, A'B'C'D'? A(2,5) A'(4,6)

T2, 1(x, y)

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).

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.

If a quadrilateral has four congruent sides and four 90 degree angles, is in considered regular?

Yes, it is a square

Which composition of transformations maps figure EFGH to figure E"F"G"H"? E (2,3) E'' (-6,-3)

a reflection across x-axis followed by a translation left 8

A composition of transformations maps ΔXYZ to ΔX"Y"Z". X(2,7) X'(-2,7),X''(-7,-2) The first transformation for this composition is____________ , and the second transformation is a 90° rotation about the origin.

a reflection across y-axis

Which figure has an order 3 rotational symmetry?

equilateral triangle

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

h

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? Across the x- axis?

rx-axis(x, y) → (x, -y)

Which triangle has 0 reflectional symmetries? isosceles, equilateral, or scalene

scalene

The image of ΔABC after a reflection across y-axis is ΔA'B'C'. If triangle ABC is a right triangle, Which triangle must be a right triangle and why?

ΔA'B'C'

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'?

(-6,-6)

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

(-y,x)

Which point would map onto itself after a reflection across the line y = -x? (2,-2) (3,3) (-4,-4)

(2,-2)

What are the coordinates of the image of vertex R after a reflection across the y-axis? R (-3,4)

(3, 4)

A(2,3) is reflected over line y=x What are the coordinates of A'?

(3,2)

The rule T5, -0.5 • RO, 180°(x, y) is applied to ΔFGH to produce ΔF"G"H". F(-1,2) What are the coordinates of vertex F" of ΔF"G"H"?

(4, -1.5)

What are the coordinates of the image of vertex D after a reflection across the x-axis? D (5,-3)

(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

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

3

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

360/n=18 so n = 20

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

360°

The image of parallelogram PQRS after a reflection across X axis is parallelogram P'Q'R'S'. Z is on the x-axis midway between R and R prime. If RR' = 12, then RZ =

6

Square A"B"C"D" is the final image after the rule T-4, -1 • RO, 90°(x, y) was applied to square ABCD. A''(-2,2) What are the coordinates of vertex A of square ABCD?

A (2,-1)

The rule ry = x • T4, 0(x, y) is applied to trapezoid ABCD to produce the final image A"B"C"D". What are the coordinates of A'' given A (2,7)

A'(7,2) A'' (11,2)

ΔA'B'C' was constructed using ΔABC and line segment EH. EH is the line of reflection. 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'.

Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?A(-2,1) A' (-1,2) A'' (-.5,1)

Reflected across line y=-x, then dilated by a factor of 1/2

If a trapezoid is dilated by a factor of 2, are what do we know about trapezoid ABCD and its translated image, A'B'C'D'?.

They are similar and the trapezoid is bigger.

Figure WXYZ is transformed using the rule ry-axis • T-4, 2(x, y). Point W of the pre-image is at (1, 6). Remember T is for translation. What are the coordinates of point W" on the final image?

W' (-1,6) W'' (-5, 8)

Does T have a line of reflectional symmetry?

Yes, vertical through the middle

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

a

A composition of transformations maps ΔKLM to ΔK"L"M". K (2,7) K'(7,-2) K''(10, -5) The first transformation for this composition is______, and the second transformation is a translation down 3 and 3 to the right

a 270 rotation about point p

What is the final transformation in the composition of transformations that maps pre-image ABCD to image A"B'C"D"? B(2,3) B'(4,6) B''(6,-4)

a 270° rotation about the origin

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 RSTUV to figure R"S"T"U"V"?

a reflection across line n followed by a 270° rotation about point P

What is the final transformation in the composition of transformations that maps pre-image GHJK to image G'H"J"K"? G(4,3) G'(-3,4) G'' (4,2)

a rotation of 90 degrees followed by a translation of 7 right and 2 down

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

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

reflected over y-axis

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

reflection across the line y=-x

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). A'(-5,1)B'(11,-2)C'-5,4) D'(3,1) What are the coordinates of the pre-image.

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

The rule ry-axis • RO, 90°(x, y) is applied to ΔABC. A(1,3) What are the coordinates of A'' in the final image?

(-3,-1)

Which point would map onto itself after a reflection across the line y = -x? (2,7) (-4,0), (-6, 3)

(-4, 0)

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)

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)

What is the pre-image of vertex A' if the image shown on the graph was created by a reflection across the y-axis? A(6,8)

(-6, 8)

Figure ABCD was reflected across the x-axis to create figure A'B'C'D'. B (-8,2) 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'. F' = (4,-2) What are the coordinates of the pre-image of F'?

(2, -4)

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 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)

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)

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

(x, y) → (y, -x)

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

(x,y) > (-y,x)

What is the degree of rotational symmetry for a rhombus?

180 degrees

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

270 degrees counterclockwise or 90 degrees clockwise

Quinton tried to transform triangle FGH according to the rule (x, y) → (-y, x). Which best describes his attempt?F(2,3) G(-4,7) H (1,-4) F'(-3,2) G'(-7,-4) H'(4,1)

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

Which statements must be true about the reflection of ΔXYZ across ?

It is isometric

What are the coordinates of L' after represents the image of trapezoid LMNP after a reflection across the x-axis? L(2,7)

L' (2,-7)

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)

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?

R0, 270° R0, -90°

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?

R0, 90° R0, -270°