Question

Circle A has center of (2, 8), and a radius of 2 and circle B has a center of (5, 4), and a radius of 10. What steps will help show that circle A is similar to circle B
1. Translate circle A using the rule (x − 3, y + 4).
2. Rotate circle A 270° about the center.
3. Reflect circle A over the line x=1
4. Dilate circle A by a scale factor of 5.

Answer 1

Answer:

1. Translate circle A using the rule (x − 3, y + 4).

4. Dilate circle A by a scale factor of 5

Step-by-step explanation:

we know that

All circles are similar figures

step 1

Translate the center of circle A to the center of circle B

we have

A(2,8) -----> B(5,4)

so

The rule of the translation is

(x,y) ----> (x+a,y+b)

(2,8) ----> (2+a,8+b)

2+a=5 ----> a=5-2=3

8+b=4 ---> b=4-8=-4

therefore

The rule of the translation is

(x,y) ----> (x+3,y-4)

step 2

Divide the radius of circle B to the radius of circle A to find out the scale factor

10/2=5

so

Multiply the radius of circle A by the scale factor to obtain the radius of circle B

therefore

Dilate circle A by a scale factor of 5