# Math Question (Similarity)?

Circle O has a center of (5,5) and a radius 4. Circle P has a center of (3,-1) and a radius of 5. How do you describe how circle O can be transformed to show that circle P is similar to circle O?

Relevance
• Circle P must be a dilation image of circle O by scale factor 5/4, the ratio of their radii. To find the center of dilation, dilate O with respect to P by factor 5.

5(5) - 4(3) = 13

5(5) - 4(-1) = 29

Let Q(13, 29) be the center of dilation. Circle P is the image of circle O, dilated with respect to Q with scale factor 5/4. • 1) Translate by (-5,-5), scale by 5/4 centred at (0,0), translate by (3,-1) {Red}

2) Scale by 5/4 centred at (0,0), translate by (-13/4,-15/2) {Blue}

3) Translate by (-13/5, -29/5) and scale by 5/4 centred at (0,0) {Green}

• I assume you desire them to have the same center...thus move P 2 units to the right and up 6 units....x ---> x - 2 & y --> y - 6

• Circle O:

(x-5)^2 + (y-5)^2 = 16

Circle P:

(x - 3)^2 + (y+1)^2 = 25

......