How will the area of the circle change if it is dilated by a scale factor of 1/2

 The area of the dilated circle will be one-forth of the area of the original circle.

Step-by-step explanation:  We are given to find the change in area of a circle if it is dilated by a scale factor of half.

Let r represents the RADIUS and A represents the AREA of the circle before dilation.

And, r' represents the radius and A' represents the AREA of the circle after dilation.

So, we get

In case of a circle, scale factor is the ratio of the radius of the dilated circle to the radius of the original circle.

That is,

Therefore, the area of the dilated circle will be

Thus, the area of the dilated circle will be one-forth of the area of the original circle.

step-by-step :