Question

Determine which of the transformations applied to Circle A could be used to prove Circle A is similar to Circle B. Select Yes or No for each transformations.

THE ANSWER I PUT WAS WRONG!!!

Answer 1

Explanation:

Circle A has center (-2, 3)

Circle B has center (2, -2)

Circle A can be mapped to Circle A' by a translation:

Center Rule of translation New center

(x, y) (x+4, y-5)

A(-2, 3) A'(-2+4, 3-5) A'(2, -2)

Circle A with radius r 1=2

Circle B with radius r 2=3

Scale factor= r 2/r 1 = 3/2 = 1.5

Since any two circles can be translated to have the same center, the dilation r2/r1 proves the circles are similar where r1 and r2 are the radii of the circles.

The Circle A' and circle B both have center (2, -2). Then circle A' can be mapped to circle B by a dilation with center (2, -2) and a scale factor 3/2=1.5. So circle A and circle B are similar.

Therefore: Translation right 4, down 5, and then a dilation of 1.5 is true.

Translation down 5, right 4, and then a dilation of 1.5 is true.