The vertices of △ ABC are located at A(4,8), B(8,0), and C(-8,4). Which sequence of transformations of △ ABC results in △ A′′B′′C′′?

Rotate △ ABC 90° counterclockwise around the origin. Dilate the image by a scale factor of 1/4 with a center of dilation at the origin.

Rotate △ ABC 90° clockwise around the origin. Dilate the image by a scale factor of 4 with a center of dilation at the origin.

Rotate △ ABC 90° counterclockwise around the origin. Dilate the image by a scale factor of 4 with a center of dilation at the origin.

Rotate △ ABC 90° clockwise around the origin. Dilate the image by a scale factor of 1/4 with a center of dilation at the origin.

The center of dilation is important because

it's the location from which the dilation occurs.

All of the corresponding points of the image and pre image are on the lines radiating from the Center of Dilation.

it's a fixed point on the plane about which all points are expanded or contracted.

Dilations and Similarity in the Coordinate Plane

Quiz

•

Mathematics

•

8th Grade

•

Practice Problem

•

Hard

•

CCSS

8.G.A.3, 8.G.A.4, HSG.CO.A.2

+3

Standards-aligned

Anthony Clark

FREE Resource

15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

A scale factor of less than one means

that the image will be larger than the pre-image.

That the image will be the same as the pre-image.

That you need to subtract that amount off of each side.

That the image will be a reduction of the pre-image.

Tags

CCSS.8.G.A.3

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Triangle REP has the coordinates
R(1, 5), E(–4, –4) and P(6, –4). If the image, R'E'P', has the coordinate
R'(3, 15), find E' and P'.

E'(-12, -12) P'(18, -12)

E'(12, 12) P'(-18, 12)

E'(0.3, 2.7) P' (2, -1.3)

Tags

CCSS.8.G.A.3

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

When the scale factor of a dilation is between 0 and 1, the dilation is a reduction (shrinks).

True

False

Tags

CCSS.8.G.A.3

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Point B (-10,-6) is dilated with a scale factor of 1/2 and the center of dilation at the origin. What are the coordinated of B'?

(5,3)

(20,12)

(-20,-12)

(-5,-3)

Tags

CCSS.8.G.A.3

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Figure DMPN is dilated to form figure D'M'P'N. What is the scale factor?

2

3

1/3

1/2

Tags

CCSS.8.G.A.3

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Triangle ABC is dilated using a scale factor of 1/2. The center of dilation is at the origin. What are the new coordinates of point A'?

(-3, 3)

(-12, 12)

(-2, 2)

Tags

CCSS.8.G.A.3

7.

DRAG AND DROP QUESTION

1 min • 1 pt

Finish the following similarity statement: Figure DEFGHI ∼ Figure (a)

DEFGHI

D'E'F'G'H'I'

ABCDEF

A'B'C'D'E'F'

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

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Dilations and Similarity in the Coordinate Plane

15 questions

A scale factor of less than one means

Triangle REP has the coordinates
R(1, 5), E(–4, –4) and P(6, –4). If the image, R'E'P', has the coordinate
R'(3, 15), find E' and P'.

When the scale factor of a dilation is between 0 and 1, the dilation is a reduction (shrinks).

Point B (-10,-6) is dilated with a scale factor of 1/2 and the center of dilation at the origin. What are the coordinated of B'?

Figure DMPN is dilated to form figure D'M'P'N. What is the scale factor?

Triangle ABC is dilated using a scale factor of 1/2. The center of dilation is at the origin. What are the new coordinates of point A'?

Finish the following similarity statement: Figure DEFGHI ∼ Figure (a)

Figures A, B, C, and D are drawn. The center of dilation is point E. Which of the following figures are similar to figure A? Choose all correct answers.

Triangle EFG is drawn on the coordinate plane. The triangle is dilated by a scale factor of 1/3, with the center of dilation at the origin, to form triangle E'F'G'. Then, triangle E'F'G' is translated 3 units to the right to form triangle E''F''G''. What is the coordinate of E'' ?

Two figures can be similar if they have the _ shape but _ size.

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Dilations and Similarity in the Coordinate Plane

15 questions

A scale factor of less than one means

Triangle REP has the coordinates R(1, 5), E(–4, –4) and P(6, –4). If the image, R'E'P', has the coordinate R'(3, 15), find E' and P'.

When the scale factor of a dilation is between 0 and 1, the dilation is a reduction (shrinks).

Point B (-10,-6) is dilated with a scale factor of 1/2 and the center of dilation at the origin. What are the coordinated of B'?

Figure DMPN is dilated to form figure D'M'P'N. What is the scale factor?

Triangle ABC is dilated using a scale factor of 1/2. The center of dilation is at the origin. What are the new coordinates of point A'?

Finish the following similarity statement: Figure DEFGHI ∼ Figure ​ (a)

Figures A, B, C, and D are drawn. The center of dilation is point E. Which of the following figures are similar to figure A? Choose all correct answers.

Triangle EFG is drawn on the coordinate plane. The triangle is dilated by a scale factor of 1/3, with the center of dilation at the origin, to form triangle E'F'G'. Then, triangle E'F'G' is translated 3 units to the right to form triangle E''F''G''. What is the coordinate of E'' ?

Two figures can be similar if they have the _______ shape but _______ size.

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Triangle REP has the coordinates
R(1, 5), E(–4, –4) and P(6, –4). If the image, R'E'P', has the coordinate
R'(3, 15), find E' and P'.

Finish the following similarity statement: Figure DEFGHI ∼ Figure (a)

Two figures can be similar if they have the _ shape but _ size.