Question

The circle P has center P and radius w. The Circle Q has center Q and radius m.

How can transformations be used to prove that circle P is similar to circle Q?

Answer 1

now try again by moving circle p

Answer 2

Transformations can be used to prove that circle P is similar to circle Q by showing that the circles can be translated, rotated, and dilated to exactly match one another.

First, translate circle Q so that its center Q matches the center P of circle P. This translation will ensure that the two circles have the same center.

Next, rotate circle Q so that its radius lines up with the radius of circle P. This rotation will ensure that the two circles have the same orientation.

Finally, dilate circle Q so that its radius m matches the radius w of circle P. This dilation will ensure that the two circles have the same size.

After performing these transformations, it will be clear that circle P and circle Q are congruent to each other, demonstrating that they are similar circles.

Answer 3

To prove that circle P is similar to circle Q, we can use transformations by moving circle P instead of circle Q.

First, translate circle P so that its center P matches the center Q of circle Q. This translation will ensure that the two circles have the same center.

Next, rotate circle P so that its radius aligns with the radius of circle Q. This rotation will ensure that the two circles have the same orientation.

Finally, dilate circle P so that its radius w matches the radius m of circle Q. This dilation will ensure that the two circles have the same size.

After performing these transformations on circle P, it will show that circle P and circle Q can be mapped onto each other, demonstrating that they are similar circles.