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Question 1138017: Triangle ABC was rotated 90 degrees clockwise. It then underwent a dilation centered at the origin with a scale factor of 4. Triangle A'B'C' is the resulting image. Is the perimeter of A'B'C' <,>, or = to the perimeter of ABC?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The rotation will not change the perimeter since the three sides will remain the same length. Put another way, the distances are kept the same. Imagine you are looking through the viewpoint of a camera. If you rotate the camera and keep the triangle still, then the illusion of rotation will happen even though the triangle doesn't move at all. This is one way to see how rotations do not affect distances/lengths.
The dilation will alter the image. The scale factor 4 means each side is 4 times larger.
Let's say that each side of triangle ABC is a,b, and c. The perimeter would be
P = a+b+c
since you add up all the sides of the triangle
Now scale each side with a factor of 4. Each side will get 4 times larger
a ---> 4a
b ---> 4b
c ---> 4c
Compute the new perimeter
Q = perimeter of A'B'C'
Q = side1+side2+side3
Q = 4a+4b+4c
Q = 4(a+b+c)
Q = 4*P
where P was the perimeter of the old original triangle ABC. We see that Q is 4 times larger than P.
So that's why the perimeter of A'B'C' is larger than the perimeter of ABC
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