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Grade 8 Mathematics EOG (GSE) Quiz Answer KeyGeometry - (MGSE8.G.4 ) Similar 2-D Figures

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

reflect across the x-axis and then translate up 2 units

Determine which rectangle was transformed to result in rectangle E.

A) rectangle A

B) rectangle B

C) rectangle C

D) rectangle D

Explanation:If rectangle C is reflected across the x-axis and then translated up 2 units, it will map directly on top of rectangle E.

2)

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How was ABCDEFGH transformed to A'B'C'D'E'F'G'H'?

A) dilated by a scale factor of 1

3

B) dilated by a scale factor of 1

2

C) dilated by a scale factor of 2

D) dilated by a scale factor of 3

Explanation:ABCDEFGH was dilated by a scale factor of 3. Every coordinate was multiplied by 3 causing a dilation.

3)

Four rectangles are shown in the diagram. For which dilation is the ratio of the side lengths 1:3?

A) D to C

B) D to B

C) C to B

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D) B to A

Explanation:The solution is D to B. The dimensions of rectangle D are 2 x 3 and the dimensions of rectangle B are 6 x 9. This results in a ratio of1:3.

4)

Describe the transformation that maps the pre-image A to the image A'.

A) translated 9 units up and then reflected across the y-axis

B) translated 6 units to right and then translated 9 units up

C) translated 9 units to right and then translated 6 units up

D) translated 6 units to the right and then reflected across the x-axis

Explanation:When translated 6 units to right and then translated 9 units up, the pre-image A maps to image A'.

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5)

Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.

A) reflect triangle A across the y-axis and then translate triangle A 5 units down

B) reflect triangle A across the x-axis and then reflect triangle A across the y-axis

C) translate triangle A 4 units down and then rotate triangle A 180° counterclockwise about the origin

D) reflect triangle A across the x-axis and then rotate triangle A 90° counterclockwise about the origin

Explanation:To map triangle A to triangle B reflect triangle A across the x-axis and then rotate triangle A 90° counterclockwise about the origin.This series of transformations will map triangle A to triangle B and illustrate the similarity between the figures.

6)

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SEPARATE IMAGES - Various dilations of square A are shown. Which square was obtained by dilating square A by the scale factor of3?

A) Square B

B) Square C

C) Square D

D) Square E

Explanation:The solution is Square E. The side lengths in Square E are 6 units. The ratio of the sides of Square E to Square A is 3:1.

7)

Describe the transformation that maps the pre-image (ΔA) to the image (ΔA').

A) a reflection over the y-axis

B) a reflection over the x-axis

C) a translation 6 units to the right

D) a translation 10 units to the right

Explanation:A reflection of the y-axis maps triangle A to triangle A'.

8)

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Rotate 90° clockwise about (0, 0) and translate 3 units right.

IMAGES NEED SEPARATING - Determine which rectangle was transformed to result in rectangle E.

A) rectangle A

B) rectangle B

C) rectangle C

D) rectangle D

Explanation:If rectangle D is rotated 90 degrees clockwise and then translated 3 units right, it will map directly on top of rectangle E.

9)

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Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.

A) rotate 90° clockwise and then translate 6 units down

B) translate 4 units down and rotate 180° about the origin

C) reflect the triangle across the y-axis and translate 4 units down

D) reflect triangle A across the x-axis and then translate 1 unit right

Explanation:To map triangle A to triangle B translate 4 units down and rotate 180° about the origin. This series of transformations will maptriangle A to triangle B and illustrate the similarity between the figures.

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10)

Describe the transformation that maps the pre-image (ΔA) to the image (ΔA').

A) a reflection of the y-axis

B) a reflection over the x-axis

C) a translation 6 units to the left

D) a translation 6 units to the right

Explanation:A translation 6 units to the right maps triangle A to triangle A'.

11)

Various dilations of square A are shown. Which square was obtained by dilating square A by the scale factor of 1

2?

A) Square B

B) Square C

C) Square D

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D) Square E

Explanation:The solution is Square C. The side lengths in Square C are 1 unit. The ratio of the sides of Square C to Square A is 1:2.

12)

Triangle ABC was dilated by 50%. What is the relationship between AC and A'C'?

A) AC = A'C'

B) AC = 5(A'C')

C) AC = 1

2(A'C')

D)1

2(AC) = A'C'

Explanation:

The solution is 1

2AC = A'C'. The side lengths in ΔABC are twice the side lengths in ΔA'B'C'.

13)

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Describe the transformations that maps triangle A to triangle A'.

A) translate 10 units up and then reflect over the y-axis

B) translate 10 units up and then reflect over the x-axis

C) translate 10 units to right and then reflect over the x-axis

D) translate 10 units to right and then reflect over the y-axis

Explanation:Translate 10 units up and then reflect over the y-axis to map triangle A to triangle A'.

14)

Describe the transformation that maps the pre-image A to the image A'.

A) translated 10 units to left and then 10 units up

B) translated 10 units to right and then 10 units down

C) translated 10 units down and then reflected across the y-axis

D) translated 10 units to right and then reflected across the x-axis

Explanation:When translated 10 units to right and then 10 units down, the pre-image A maps to image A'.

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15)

Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.

A) reflect triangle A across the y-axis and then translate triangle A 5 units down

B) reflect triangle A across the x-axis and then reflect triangle A across the y-axis

C) rotate triangle A 270° counterclockwise about the origin and then reflect triangle A across the x-axis

D) rotate triangle A 90° counterclockwise about the origin and then translate triangle A 4 units to the right

Explanation:To map triangle A to triangle B rotate triangle A 270° counterclockwise about the origin and then reflect triangle A across the x-axis.This series of transformations will map triangle A to triangle B and illustrate the similarity between the figures.

16)

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reflect across the x-axis and then rotate 90° counterclockwise about the origin

Determine which rectangle was transformed to result in rectangle E.

A) rectangle A

B) rectangle B

C) rectangle C

D) rectangle D

Explanation:If rectangle A is reflected across the x-axis and then rotated 90° counterclockwise, it will map directly on top of rectangle E.

17)

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Describe the transformations that maps triangle A to triangle A'.

A) translate 7 units to left and then reflect over the x-axis

B) translate 5 units to left and then reflect over the x-axis

C) translate 7 units to right and then reflect over the x-axis

D) translate 5 units to right and then reflect over the x-axis

Explanation:Translate 7 units to right and then reflect over the x-axis to map triangle A to triangle A'.

18)

What type of figures are shown? Which scale factor changes the small to the large version?

A) Trapezoids; 1.5

B) Trapezoids; 2

3

C) Kites; 1.5

D) Kites; 2

3

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Explanation:The solution is Kites; 1.5. The figures are kites since they are quadrilaterals with two disjoint pairs of congruent adjacent sides. Thescale factor is found by matching corresponding sides and simplifying the ratio.

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19)

The graph shows the dilation of quadrilateral MNOP with the origin as its center. Which rule describes this transformation?

A) (x, y) → (3x, 3y)

B) (x, y) → (x + 3, y +3)

C) (x, y) → (x - 3, y - 3)

D) (x, y) → (1

3x,

1

3y)

Explanation:Dilations are caused by multiplying the x- and y- coordinates of the original figure by the scale factor. In this case, quadrilateral

M'N'O'P' is 1

3 as large as quadrilateral MNOP. The coordinates of quadrilateral MNOP have been multiplied by

1

3. The rule (x, y) → (

1

3x,

1

3y) describes this transformation.

20)

If ΔAED is dilated to points A, C, and B, which statement is true?

A) ΔAED ~ ΔACB

B) ΔAED ≅ ΔACB

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C) The area of ΔAED is half the area of ΔACB

D) The perimeter of ΔAED is one-fourth the area of ΔACB

Explanation:Solution: AED ~ ACB. The side lengths in the new triangle will be twice as large as the side lengths of the original triangle. Theangles are still congruent. Therefore, the triangles are similar.

21)

Describe the transformation that maps the pre-image A to the image A'.

A) translated 10 units to right and then 10 units up

B) translated 5 units to left and then reflected across the x-axis

C) translated 10 units to right and then reflected across the x-axis

D) translated 10 units to right and then reflected across the y-axis

Explanation:When translated 10 units to right and then reflected across the x-axis, the pre-image A maps to image A'.

22)

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Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.

A) rotate 90° clockwise and then translate 6 units down

B) translate 4 units down and rotate 180° about the origin

C) reflect the triangle across the y-axis and translate 4 units down

D) reflect triangle A across the x-axis and then translate 1 unit right

Explanation:To map triangle A to triangle B reflect the triangle across the y-axis and translate 4 units down. This series of transformations willmap triangle A to triangle B and illustrate the similarity between the figures.

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23)

Describe the transformation that maps the pre-image (ΔA) to the image (ΔA').

A) a rotation 180° clockwise around the origin

B) a rotation 270° clockwise around the origin

C) a rotation 90° counterclockwise around the origin

D) a rotation 270° counterclockwise around the origin

Explanation:A rotation 270° counterclockwise around the origin maps triangle A to triangle A'.

24)

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Describe the transformation that maps the pre-image A to the image A'.

A) translated 8 units up and then reflected across the y-axis

B) translated 8 units down and then reflected across the y-axis

C) translated 1 unit to left and then rotated 180° counterclockwise around the origin

D) translated 1 unit to right and then rotated 180° counterclockwise around the origin

Explanation:When translated 1 unit to left and then rotated 180° counterclockwise around the origin, the pre-image A maps to image A'.