Question

Given two concentric circles (circles that have the same center point), with the inner circle having a radius of 1 r and the outer one having a radius of 2 r as shown, give a dilation that would map the inner circle onto the outer circle.

Answer 1

Answer:

(x, y) ⇒ (2x, 2y)

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Dilation is the increase or decrease in size of a figure. If a figure with point A(x, y) is dilated by a scale factor of k, the new location is at A'(kx, ky). If k > 1, it is an enlargement and if k < 1, it is a reduction.

Given that the inner circle has a radius of 1 r and the outer one has a radius of 2 r. To map the inner circle onto the outer circle, the inner circle would need to be enlarged. The scale factor is:

k = outer circle radius / inner circle radius = 2r / 1r = 2

A dilation with a scale factor of 2 would be needed to map the inner circle onto the outer circle.

That is:

(x, y) ⇒ (kx, ky)