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 pre-image. What is the scale factor?

-1 or 1

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 pre-image, QPR?

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

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

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

smaller than and along the same ray as