Select the sequence of rigid transformations and dilations that takes square $$ABCD$$ to square $$EFGH$$ .

Translate by the directed line segment AE. Then, rotate with center E by angle B'EF. Finally, dilate with center E by scale factor $$\frac{2}{5}$$

Translate by the directed line segment AE. Then, rotate with center E by angle B'EF. Finally, dilate with center E by scale factor $$\frac{5}{2}$$

Dilate using center E by scale factor $$\frac{2}{5}$$

Dilate using center E by scale factor $$\frac{5}{2}$$

The graphic below shows quadrilateral NXSR and its dilation, quadrilateral N’X’S’R’, with the origin as the center of dilation. Which statement is true about the quadrilaterals?

The corresponding angles of quadrilaterals NXSR and N’X’S’R’ are congruent.

The corresponding sides of quadrilaterals NXSR and N’X’S’R’ are congruent.

The corresponding angles of quadrilaterals NXSR and N’X’S’R’ are proportional.

Quadrilateral NXSR is congruent to quadrilateral N’X’S’R’.

Quadrilateral EJMX is dilated with the origin as the center of dilation using the rule (x,y)--->(2.4x, 2.4y) to create quadrilateral E’J’M’X’. What statement is true?

Quadrilateral E’J’M’X’ is larger than quadrilateral EJMX, because the scale factor is greater than 1.

Quadrilateral E’J’M’X’ is smaller than quadrilateral EJMX, because the scale factor is less than 1.

Quadrilateral E’J’M’X’ is larger than quadrilateral EJMX, because the scale factor is less than 1.

Quadrilateral E’J’M’X’ is smaller than quadrilateral EJMX, because the scale factor is greater than 1.

Which set of transformations could be used to prove the quadrilaterals are congruent?

Reflect quadrilateral ABCD across the y–axis and then rotate it 90 degrees counter clockwise.

Reflect quadrilateral ABCD across the x–axis and then reflect it across the y–axis.

Reflect quadrilateral ABCD across the y–axis and then translate it down 4 units.

Reflect quadrilateral ABCD across the x–axis and then rotate it 90 degrees counter clockwise.

Quadrilateral A is rotated 90 degrees clockwise and then dilated with a scale factor of 5 to create quadrilateral B. Which of the following statements is TRUE?

The two quadrilaterals are similar, but not congruent.

The two quadrilaterals are similar and congruent.

The two quadrilaterals are not similar or congruent.

The two quadrilaterals are congruent, but not similar.

Which of the following sequence of transformations will result in a figure that is similar to the original figure but has a SMALLER area than the original figure? Select ALL that apply.

A dilation about the origin by a scale factor of \frac{1}{3} 3 1 followed by a translation down and a rotation 90 degrees clockwise

A dilation about the origin by a scale factor of $$\frac{3}{4}$$ followed by a reflection across the x–axis and another dilation by a scale factor of $$\frac{2}{3}$$

A rotation 180 degrees about the origin followed by a dilation by a scale factor of $$\frac{9}{4}$$

A reflection across the y–axis followed by a dilation by a scale factor of 3 and then a translation 6 units up

Which of the following sequence of transformations will result in a figure that is similar to the original figure but has a LARGER area than the original figure? Select ALL that apply.

A translation 8 units right and 3 units down followed by a dilation about the origin by a scale factor of 5

A reflection across the x–axis followed by a dilation about the origin by a scale factor of 4 and then a rotation 180 degrees

A dilation about the origin by a scale factor of $$\frac{1}{2}$$ followed by a rotation 90 degrees counterclockwise and a translation left

A dilation about the origin by a scale factor of $$\frac{4}{5}$$ followed by a translation 12 units down and then another dilation about the origin by a scale factor of $$\frac{1}{10}$$

On a coordinate plane, if a figure has an angle measuring 69 degrees, which of the following statements are correct? Select THREE that apply.

If the figure is translated 15 units up, the angle will still measure 69 degrees.

If the figure is reflected across the line y = x, the angle will still measure 69 degrees.

If the figure is rotated 90 degrees about the origin, the angle will still measure 69 degrees.

If the figure is rotated 180 degrees about the origin, the angle will no longer measure 69 degrees.

Transformations with Quadrilaterals

Authored by Anthony Clark

Mathematics

8th Grade

CCSS covered

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20 questions

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MULTIPLE SELECT QUESTION

1 min • 1 pt

Quadrilaterals ABCD and A'B'C'D' are shown on the coordinate plane. Which transformation or sequence of transformations would result in ABCD being mapped on A'B'C'D'? Select all that apply.

A 180 degree rotation about the origin

A reflection across the x-axis followed by a reflection across the y-axis

A reflection across the y-axis followed by a translation up four units

A 270 degree counterclockwise rotation about the origin

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Quadrilaterals ABCD and A'B'C'D' are shown on the coordinate plane. Quadrilateral ABCD will be rotated 90 degrees counterclockwise about the origin and then reflected about the x-axis to create quadrilateral EFGH. What will the x-coordinate of H be?

-1

-2

Tags

CCSS.8.G.A.3

MULTIPLE SELECT QUESTION

1 min • 1 pt

In the image of trapezoid ABCD, the x-axis bisects the legs and the y-axis bisects the bases. What transformation(s) will map ABCD onto itself?

A 180 degree rotation about the origin

A reflection across the x-axis

A reflection across the y-axis

A reflection across a line connecting vertices A and D

A 90 degree clockwise rotation about the origin

Tags

CCSS.HSG.CO.A.3

MULTIPLE SELECT QUESTION

1 min • 1 pt

Lisa needs to transform rectangle LMNO while preserving the length of each side. Which transformation(s) could she do? Select all that apply.

Rotate 270 degrees clockwise about the origin

Reflect across the y-axis

Reflect across the line y = 2x + 1

Dilate by a scale factor of 2

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Identify the transformation.

Reflection across y axis

Reflection across x-axis

180 Rotation

Translation 2 units down

Tags

CCSS.8.G.A.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which transformation on quadrilateral ABCD produces an image that does not preserve distance between points in quadrilateral ABCD?

reflection across y = x

translation 3 units down and 4 units to the right

dilation by a scale factor of 2

rotation 270 degrees

Tags

CCSS.HSG.CO.A.2

MULTIPLE SELECT QUESTION

1 min • 1 pt

Rectangle WXYZ has its center at the origin. Which transformation could map WXYZ onto itself? Select all that apply.

Reflection across the x-axis.

180 degree rotation.

90 degree counterclockwise rotation.

Translation up two units.

Reflection across the y-axis.

Tags

CCSS.HSG.CO.A.3

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Transformations with Quadrilaterals

Quadrilaterals ABCD and A'B'C'D' are shown on the coordinate plane. Which transformation or sequence of transformations would result in ABCD being mapped on A'B'C'D'? Select all that apply.

Quadrilaterals ABCD and A'B'C'D' are shown on the coordinate plane. Quadrilateral ABCD will be rotated 90 degrees counterclockwise about the origin and then reflected about the x-axis to create quadrilateral EFGH. What will the x-coordinate of H be?

In the image of trapezoid ABCD, the x-axis bisects the legs and the y-axis bisects the bases. What transformation(s) will map ABCD onto itself?

Lisa needs to transform rectangle LMNO while preserving the length of each side. Which transformation(s) could she do? Select all that apply.

Identify the transformation.

Which transformation on quadrilateral ABCD produces an image that does not preserve distance between points in quadrilateral ABCD?

Rectangle WXYZ has its center at the origin. Which transformation could map WXYZ onto itself? Select all that apply.

The 4 points on the graph represent the points of quadrilateral ABCD. Place on the graph the 4 points after they are dilated by a scale factor of 2 using the origin as the center of dilation.

Which rule best represents the dilation that was applied to quadrilateral AJDU to create quadrilateral A’J’D’U’?

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