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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.
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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perl
 one year ago
Best ResponseYou've already chosen the best response.1all 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
 one year ago
Best ResponseYou've already chosen the best response.1If 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).

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1ok hold on i need a peice of paper.

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1ok so before you scale it b would be 7,4 right?

perl
 one year ago
Best ResponseYou've already chosen the best response.1right, we move the center of circle D to the center of circle B

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1when you scale it the 1/2 equals .5 right?.. i mean its a stupid question but you know?

perl
 one year ago
Best ResponseYou've already chosen the best response.1i also graphed the circles so you can see it visually https://www.desmos.com/calculator/eb0otly6pv

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1i mean, thats what i got when i scaled it

perl
 one year ago
Best ResponseYou've already chosen the best response.1well we are scaling all the points on the circle

perl
 one year ago
Best ResponseYou've already chosen the best response.1i 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
 one year ago
Best ResponseYou've already chosen the best response.1the circle itself is just the circumference or the boundary of the circle

perl
 one year ago
Best ResponseYou've already chosen the best response.1lets pick a point on circle B , say (1,5) https://www.desmos.com/calculator/toiyetveam

perl
 one year ago
Best ResponseYou've already chosen the best response.1now the first transformation will translate or slide the point to the right 8 units and down one unit

perl
 one year ago
Best ResponseYou've already chosen the best response.1hmm, ok maybe this idea doesn't work exactly as i envisioned, lets try something different

perl
 one year ago
Best ResponseYou've already chosen the best response.1first lets move the circle B to the origin, then scale it by a factor of 1/2

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1ok...but wouldnt it still be the origin 7,4

perl
 one year ago
Best ResponseYou've already chosen the best response.11. 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
 one year ago
Best ResponseYou've already chosen the best response.1the origin is the point (0,0) we like to call it the origin of the x y plane

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1*facepalm* of course. i knew that

perl
 one year ago
Best ResponseYou've already chosen the best response.1lets 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
 one year ago
Best ResponseYou've already chosen the best response.1ok.. how would i be able to explain this in writing?. i am not very good at turning thing into words.

perl
 one year ago
Best ResponseYou've already chosen the best response.1now 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
 one year ago
Best ResponseYou've already chosen the best response.1translate 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
 one year ago
Best ResponseYou've already chosen the best response.1the image of the three transformations is circle D. since we only used translations and scaling, the two figures are similar

perl
 one year ago
Best ResponseYou've already chosen the best response.1im not sure how detailed your teacher wants it

demonchild99
 one year ago
Best ResponseYou've already chosen the best response.1i think i got it now and it should be good! thank you

perl
 one year ago
Best ResponseYou've already chosen the best response.1briefly in words: 1. slide circle B to origin (0,0) 2. scale the circle by 1/2 3. slide it to point (7,4)
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