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?

4 Answers

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  • Pope
    Lv 7
    6 months ago

    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.

    Attachment image
  • 6 months ago

    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}

    Graph: https://www.desmos.com/calculator/j4mqaokive

  • ted s
    Lv 7
    6 months ago

    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

  • 6 months ago

    Circle O:

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

    Circle P:

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

    ......

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