Dilations

Triangle EFG is dilated with a scale factor of 1/2 to create ∆E'F'G'. The measure of ∠F' is 36°. What is m∠F?

• 18 °

• 36 °

• 72°

• 144°

Triangle CAT is the image that resulted from a dilation of triangle RED.

• (0,0)

• R

• C

• D

Triangle ABC is dilated to produce triangle A'B'C' with scale factor 3/4. Which describes the relationship between the two triangles?

• ∆A'B'C' is an enlargement of ∆ABC.

• ∆A'B'C' is a reduction of ∆ABC.

• ∆A'B'C' ≅ ∆ABC

• ∆A'B'C' is a mirror image of ∆ABC.

A triangle has vertices at (1, 1), (1, 2), and (3, 2). It is dilated by a scale factor of 3 with the origin as the center of dilation to form a similar triangle. What are the coordinates of the vertices of the image?

• (4, 1), (4, 2), (6, 2)

• (1, 4), (1, 5), (3, 5)

• (4, 4), (4, 6), (6, 5)

• (3, 3), (3, 6), (9, 6)

Given ∆ABC ~ ∆ADE with AB = 2 centimeters, BD = 3 centimeters, and DE = 10 centimeters.

What is the length of BC ?

• 6 2/3 centimeters

• 5 centimeters

• 4 centimeters

• 6 centimeters

What is the name of the point from which a dilation is drawn?

• the vertex

• the center of dilation

• the origin of dilation

• the corner

A triangle is dilated with a center of dilation at the origin. Point P is on the figure and P' is the corresponding point on the image of the dilation. Point P is at (22, 3) and P' is at (28, 12). What is the scale factor?

• 2

• 4

• 6

• 9

Parallelogram ABCD is transformed to create parallelogram A'B'C'D'. Which shows the sequence of transformations needed to create A'B'C'D'?

• a dilation about the origin with a factor of 3/2 and a translation 3 units to the right.

• a dilation about the origin with a factor of 2/3 and a translation 3 units to the right.

• a dilation about the origin with a factor of 3/2 and a translation 3 units to the left

• a dilation about the origin with a factor of 2/3 and a translation 3 units to the left.

Which must be true of a scale factor of a dilation if the image is smaller than the original figure?

• The scale factor is negative.

• The scale factor is between 21 and 0.

• The scale factor is between 0 and 1.

• The scale factor is positive.

Given ∆RST is similar to ∆UVW with RT = 9 inches, UW = 5.4 inches, and RS = 6 inches.

Which is the length of UV ?

• 3.6 inches

• 2.4 inches

• 8.1 inches

• 4 inches