Dilations

What are the coordinates of the image of the point (-3, 6) after a dilation with a center of (0, 0) and scale factor of 1/3?

(-1, 2)

What are the coordinates of the image of the point (2, -4) after a dilation with a center of (0, 0) and scale factor of 4?

(8, -16)

Under a dilation centered at the origin, the image is congruent to the preimage. What is the scale factor?

-1 or 1

Determine the value of x. DO,k(x, 9) → (-10, -6)

15

Determine the value of y.

2.5

Q'P'R' is an image created by a dilation centered at the origin with a scale factor K=1/4. The vertices of Q'P'R' are Q'(-2, 1), P'(1 ,2), and R'(-1, 3). What are the coordinates of the vertices of the preimage, QPR?

Q(-8, 4), P(4, 8), R(-4, 12)

Under a dilation, a figure is enlarged and its orientation is preserved. Choose the statement that best describes the dilation.

The image is along the same ray as the preimage but is farther from the center of dilation.

After a dilation with a center of (0, 0), a point was mapped as (4, -6) → (12, y). A student determined y to be -2. Evaluate the student's answer.

The student incorrectly divided by the scale factor instead of multiplying by it.

After a dilation with a center of (0, 0), a point was mapped as (1, 4) → (4, y). A student determined y to be 16. Evaluate the student's answer.

The student is correct.

Figure A is the preimage. Which figure is the image of figure A after a dilation with a scale factor of 2 and a center of (0, 0)?

figure T

Which of the following scale factors will result in an enlargement?

k < -1

Calculate the scale factor.

k=11/9

Line AB has a length of 5 cm. The line segment is dilated to produce line A'B', which has a length of 2 cm. Find the scale factor of the dilation.

k=2/5

Calculate the scale factor.

k=5/7

Let line C'P' be the image of line CP after a dilation. The equation to calculate the scale factor, k, is _____.

k=line C'P'/line CP

When applied to a triangle, a dilation with a positive scale factor does not preserve __________.

length

In a dilation with a scale factor of 3/4, the image is __________ the preimage.

smaller than and along the same ray as