Graph the image of the figure after a dilation with the scale factor of 3 centered at the origin.

Shown below

Dilation is when you stretch something by the same amount in two perpendicular directions. In other words, dilation changes size, not overall shape. Dilation factors greater than one makes the shape greater while dilation factors less than one makes the shape smaller. To dilate a shape with a certain scale factor centered at the origin, we just need to multiply each point by that scale factor. Since the figure is a rectangle, we just need to take the vertices of this figure, therefore:

A(-2,1)

B(1,1)

C(-2,3)

D(1,3)

So, the new points will be:

A'(-2x3, 1x3) = A'(-6, 3)

B'(1x3, 1x3) = B'(3, 3)

C'(-2x3, 3x3) = C'(-6, 9)

D'(1x3, 3x3) = D'(3, 9)

The new shape is shown below. As you can see, the new rectangle is greater than the original because the scale factor is greater than one.

c-4 is the final answer! : )