Question

What scale factor was used to make the image A'B'C?

Answer 1

Explanation:

Take scale 1box=1unit

• BC=1units

And

• B'C'=2units

Scale factor

• k=B'C'/BC
• 2/1
• 2

Answer 2

-2

Explanation:

Please note that image ABC in the question has not been dilated about the origin.

The scale factor of the dilated image is -2 as:

• the sides of A'B'C are twice those of ABC.
• A'B'C is on the other side of the given center of dilation (0, 0).
• A'B'C is upside down.

When dilating about a point, the distances from the center of dilation to each vertex are multiplied by the scale factor (see attachment).

When dilating about the origin, we simply multiply the x and y values of the vertices of the pre-image by the scale factor. Therefore, the dilation of image ABC by scale factor -2 is:

Pre-image:

• A = (3, 2)
• B = (1, 3)
• C = (1, 4)

Dilated image:

A' = (3 × -2, 2 × -2) = (-6, -4)

B' = (1 × -2, 3 × -2) = (-2, -6)

C' = (1 × -2, 4 × -2) = (-2, -8)