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)

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

Step-by-step 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)

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11-1 > 1-1+a

-12 > a