demonchild99
  • demonchild99
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.
Geometry
katieb
  • katieb
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perl
  • perl
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
perl
  • perl
http://www.mathsisfun.com/geometry/transformations.html
perl
  • perl
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).

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demonchild99
  • demonchild99
ok hold on i need a peice of paper.
demonchild99
  • demonchild99
ok so before you scale it b would be 7,4 right?
perl
  • perl
right, we move the center of circle D to the center of circle B
demonchild99
  • demonchild99
when you scale it the 1/2 equals .5 right?.. i mean its a stupid question but you know?
perl
  • perl
yes thats correct
perl
  • perl
i also graphed the circles so you can see it visually https://www.desmos.com/calculator/eb0otly6pv
demonchild99
  • demonchild99
3.5,2 and cool!
demonchild99
  • demonchild99
i mean, thats what i got when i scaled it
perl
  • perl
well we are scaling all the points on the circle
perl
  • perl
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.
perl
  • perl
the circle itself is just the circumference or the boundary of the circle
perl
  • perl
lets pick a point on circle B , say (1,5) https://www.desmos.com/calculator/toiyetveam
perl
  • perl
now the first transformation will translate or slide the point to the right 8 units and down one unit
perl
  • perl
hmm, ok maybe this idea doesn't work exactly as i envisioned, lets try something different
demonchild99
  • demonchild99
lol. ok
perl
  • perl
first lets move the circle B to the origin, then scale it by a factor of 1/2
demonchild99
  • demonchild99
ok...but wouldnt it still be the origin 7,4
perl
  • perl
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)
perl
  • perl
the origin is the point (0,0) we like to call it the origin of the x y plane
demonchild99
  • demonchild99
*facepalm* of course. i knew that
perl
  • perl
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
demonchild99
  • demonchild99
ok.. how would i be able to explain this in writing?. i am not very good at turning thing into words.
perl
  • perl
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
perl
  • perl
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)
perl
  • perl
the image of the three transformations is circle D. since we only used translations and scaling, the two figures are similar
perl
  • perl
im not sure how detailed your teacher wants it
demonchild99
  • demonchild99
i think i got it now and it should be good! thank you
perl
  • perl
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)
perl
  • perl
your welcome :)

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