Question

If triangle ABC is defined by the coordinates A(-4, -4), B(2, -2), C(0, 4) is dilated by a scale factor of 1 2 , with resulting vertex A' at (-2, -2). What is the center of the dilation? A) (0, 0) B) (0, 2) C) (0, 4) D) (-4, -4)

Answer 1

The center of the dilation is (0 , 0) ⇒ answer A

Explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.

- It can become larger or smaller, but the shape of the

figure does not change.

- The scale factor, measures how much larger or smaller

the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The dilation has a center which we measure all the size from it

- If the center is the origin we multiply the scale factor by the

coordinates of the points

- For a dilation not at the origin, we measure the distances.

* In the problem

- In ΔABC:

∵ A = (-4 , -4) , B = (2 , -2) and C = (0 , 4)

∵ The scale factor is 1/2

∵ A' = (-2 , -2)

- If we multiply A (-4 , -4) by the scale factor 1/2, about the center origin

then the image A' = (-2 , -2)

∴ The center of the dilation is (0 , 0)