Question

Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B?

Translate circle A using the rule (x + 4, y + 3).
Rotate circle A 45° about the center.
Dilate circle A by a scale factor of 4.
Reflect circle A about the origin.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Circle A can be made similar to circle B by dilating circle A by scale factor 4.

Circles can be made similar by performing transformations such as dilations, translation, etc.

The given parameters are:

Circle A

$(x,y) = (6,7)$ --- center

$r=4$ --- radius

Circle B

$(x,y) = (2,4)$  --- center

$r = 16$ --- radius

To do this, we simply make both circles have the same radius.

Given that:

$r_A=4$ --- radius of A

$r_B = 16$ --- radius of B

Dilating the radius of A by 4 will make both circles have the same radius.

i.e.

$R = r_A * 4$

$R = 4 * 4$

$R = 16$

Now, the new radius of A is 16; same as B

Both circles now have the same radius, means that the circles are similar.

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