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demonchild99

  • one year ago

Circle B has a center of (−1, 5) and a radius of 4. Circle D has a center of (7, 4) and a radius of 2. Prove that the two circles are similar.

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  1. perl
    • one year ago
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    all circles are similar, but if you want to prove this rigorously. two figures are similar if you can translate/rotate/scale one figure to another

  2. perl
    • one year ago
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    http://www.mathsisfun.com/geometry/transformations.html

  3. perl
    • one year ago
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    If one shape can become another using only Turns, Flips and/or Slides, then the two shapes are called Congruent. Two shapes are Similar if you need to Resize for one shape to become another (you may also Turn, Flip and/or Slide).

  4. demonchild99
    • one year ago
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    ok hold on i need a peice of paper.

  5. demonchild99
    • one year ago
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    ok so before you scale it b would be 7,4 right?

  6. perl
    • one year ago
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    right, we move the center of circle D to the center of circle B

  7. demonchild99
    • one year ago
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    when you scale it the 1/2 equals .5 right?.. i mean its a stupid question but you know?

  8. perl
    • one year ago
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    yes thats correct

  9. perl
    • one year ago
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    i also graphed the circles so you can see it visually https://www.desmos.com/calculator/eb0otly6pv

  10. demonchild99
    • one year ago
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    3.5,2 and cool!

  11. demonchild99
    • one year ago
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    i mean, thats what i got when i scaled it

  12. perl
    • one year ago
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    well we are scaling all the points on the circle

  13. perl
    • one year ago
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    i see what you did, you scaled the center of the circle, but note that the center of the circle is not actually a part of the graph.

  14. perl
    • one year ago
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    the circle itself is just the circumference or the boundary of the circle

  15. perl
    • one year ago
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    lets pick a point on circle B , say (1,5) https://www.desmos.com/calculator/toiyetveam

  16. perl
    • one year ago
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    now the first transformation will translate or slide the point to the right 8 units and down one unit

  17. perl
    • one year ago
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    hmm, ok maybe this idea doesn't work exactly as i envisioned, lets try something different

  18. demonchild99
    • one year ago
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    lol. ok

  19. perl
    • one year ago
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    first lets move the circle B to the origin, then scale it by a factor of 1/2

  20. demonchild99
    • one year ago
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    ok...but wouldnt it still be the origin 7,4

  21. perl
    • one year ago
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    1. translate center of circle B to the origin (0,0) 2. scale circle B by a factor of 1/2 3. translate center of circle B to center (7,4)

  22. perl
    • one year ago
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    the origin is the point (0,0) we like to call it the origin of the x y plane

  23. demonchild99
    • one year ago
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    *facepalm* of course. i knew that

  24. perl
    • one year ago
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    lets graph it on desmos calculator in steps. 1. Draw circle B https://www.desmos.com/calculator/q6dcuoxeex 2. Translate circle B to the origin (0,0) https://www.desmos.com/calculator/l10dl6w4ux 3. scale circle B by a factor of 1/2 https://www.desmos.com/calculator/1vmus35noh 4. translate circle B to center (7,4) https://www.desmos.com/calculator/3n58wcsjix now the graph in step 4 is the same as circle D

  25. demonchild99
    • one year ago
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    ok.. how would i be able to explain this in writing?. i am not very good at turning thing into words.

  26. perl
    • one year ago
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    now in step 2, when you scaled the center (0,0) by 1/2, thats still (0,0), since a half of zero is 0. but technically the center is not part of the graph

  27. perl
    • one year ago
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    translate circle B to origin (x,y) -> (x+1, y - 5) scale the moved circle B by 1/2 (x,y) -> (1/2 * x , 1/2 * y) translate the scaled circle B to (7,4) (x,y) -> (x +7, y + 4)

  28. perl
    • one year ago
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    the image of the three transformations is circle D. since we only used translations and scaling, the two figures are similar

  29. perl
    • one year ago
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    im not sure how detailed your teacher wants it

  30. demonchild99
    • one year ago
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    i think i got it now and it should be good! thank you

  31. perl
    • one year ago
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    briefly in words: 1. slide circle B to origin (0,0) 2. scale the circle by 1/2 3. slide it to point (7,4)

  32. perl
    • one year ago
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    your welcome :)

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