SIMILARITY TRANSFORMATION: DILATION

DO,-1.2 of Z is

(-1, 1)

A dilation maps (4, 6) to (2, 3). Under the same dilation, (-1,3) would be mapped to

(-1/2, 3/2)

DO,-1.2 of X is

(-2, 0)

What is the image of (-1, 1) after a dilation of 2?

(-2, 2)

DO,-2(x, y) → (3, 5). The point (x, y) is

(-3/2, -5/2)

What are the coordinates of M' after triangle MNO is reflected over the y-axis, and rotated 90 degrees clockwise with the origin as the center of rotation?

(0, -6)

What are the coordinates for the origin of the coordinate plane?

(0, 0)

DO,1 of X is

(4, 0)

DZ,2 of X is

(6, 2)

DO,2 of Y is

(6, 4)

DO,K = (6, 12) → (3, 6) The scale factor is

1/2

What is the value of y?

16.5 ft

DO,K = (5, 0) → (10, 0) The scale factor is:

2

The image of (6, 9) under a dilation is (4, 6). The scale factor is

2/3

DO,K = (0, 2) → (0, 6) The scale factor is

3

Malaya is making a collage of her birthday party photos and she wants to add an 8 x 10 inch. photo. Since there is not enough space left on the collage, she must trim the photo. If the scale factor from the original to the trimmed photo is 5:4, the new dimensions of the photo are ______.

6.4 x 8 in

Allison claims that the ΔABQ is similar to ΔRPQ, given that AB and PR are parallel. Which of Allison's claims supporting her argument are correct? Select all that apply.

<BAQ = <QRP because they are alternate interior angles. <1 = <2 because they are vertically opposite angles.

Use ΔJKL and ΔMPN to determine whether Don's claim is true or false. Which of the following should Don use to prove the triangles are similar?

AA

A dilation centered at the origin is applied to the line y = 3x + 5. What is true about the image of the line?

It is another line parallel to y = 3 x + 5.

If you wish to show that two triangles are similar, which statement(s) is correct? You may choose more than one correct answer.

It is enough to show that all three pairs of corresponding sides are in the same ratio. It is enough to show that two pairs of corresponding angles are congruent.

In the diagram below, side XY is parallel to side X'Y'. There is a dilation centered at ________ with a scale factor of ________ which will transform triangle XYZ into triangle X'Y'Z.

Point Z; 1.50

Select all that apply. The following graph shows an ellipse that suffered several transformations. Which of the following two sets of combinations of transformations could map ellipse 1 into ellipse 2? You may choose more than one correct answer.

Reflection along y = -x, and translation 6 units to the right Rotation of 90° clockwise by the origin O, and translation 2 units to the left

The pentagon ABCDE is dilated to the image A'B'C'D'E' with the center of the dilation at the origin. Select all true statements.

The scale factor of the dilation is 1/2. The line CD is not parallel to the line C'D' because CD passes through the center of the dilation.

A dilation is applied to a triangle such that the sides of the image are 1.5 times the length of their corresponding sides in the original triangle.

Then the angles of the image must be congruent to the corresponding angles in the original triangle.

Two right triangles are shown below. Which statement is true?

There is no dilation transforming triangle I into triangle II.

A triangle has vertices at O(0, 0), A(1, 0), and B(0, 1). A dilation centered at (1, 0) is applied to the triangle. __________ of the sides lie on the same line as their respective images.

Two

If a dilation is applied to a triangle, then the image must be _____.

a larger or smaller triangle.

Which of the following does not describe a dilation?

isometry

Choose the correct description. The angles of one triangle are in ratio x : 2x : 5x and the angles of another triangle are in the ratio x : 2x : 3x . The two triangles are ________ because at least one pair of corresponding angles are ________.

not similar; different

DO,K = (9, 6) → (3, 2) The scale factor is:

1/3