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.

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)

andromache andromache · Answer 2 · 2022-03-04T11:40:28+01:00

The dilation should be (x, y) ⇒ (2x, 2y)

What is transformation and dilation:

Transformation refers to the point movement that starts from beginning location to the new location. The dilation refers to the increment or decrement of the figure size.

Here,

The scale factor should be calculated by dividing the outer circle radius from the inner circle radius

[tex]= 2r\div 1r[/tex]

= 2

Therefore, The dilation should be (x, y) ⇒ (2x, 2y)

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