Question

1.As shown in the diagram below, Circle A as a radius of 3 and circle B has a radius of 5.Use transformations to explain why circles A and B are similar.2. Which can be accomplished using a sequence of similarity transformations?|. mapping circle O onto to circle P so that 01 matches P1||. mapping circle P onto circle O so that P1 mathches O1A. | only B. || onlyC. both | and || D. neither | or ||

Answer 1

They are similar. See the below for the proof.

Step-by-step explanation:

Radius of circle A = 3

Radius of circle B = 5

radius A < radius B

radius B > radius A

So we move the circle with the smaller radius into the circle with the larger radius in such a way that the center of both circles align with each other.

To increase the size of circle B, we apply dilation one of the form of transformation.

In dilation, the original image is increased or decreased by a scale factor.

Since All points from the circumference of the circle are of equal distance from the center of the circle, the radius is used to determine the scale factor

radius of small circle × scale factor = radius of big circle

scale factor = big radius/small radius

scale factor = 5/3

So considering the two radius are apart, and we need to move them and aligh them, there will be translation. This is also a form of transformation. It causes movement up, down, left or right.

After the translation comes the dilation.

Hence, it is proven the circles are similar after the two transformations are done.