SOLUTION: In a triangle ABC, A (4 , 1), B (6 , 1) , C (4 , 6). In a triangle A'B'C', A' (0 , -1), B' (-2 , -1), C' (0 , -6). Find the angle of rotation and centre of rotation.

Algebra ->  Coordinate-system -> SOLUTION: In a triangle ABC, A (4 , 1), B (6 , 1) , C (4 , 6). In a triangle A'B'C', A' (0 , -1), B' (-2 , -1), C' (0 , -6). Find the angle of rotation and centre of rotation.      Log On


   

Question 399366: In a triangle ABC, A (4 , 1), B (6 , 1) , C (4 , 6).
In a triangle A'B'C', A' (0 , -1), B' (-2 , -1), C' (0 , -6). Find the angle of rotation and centre of rotation.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
A (4 , 1), B (6 , 1) , C (4 , 6).
In a triangle A'B'C', A' (0 , -1), B' (-2 , -1), C' (0 , -6). 



Let's connect corresponding points:






To find the center or rotation find the midpoint P of either

AA', BB', or CC'

If you find the midpoint of AA' using the formula

M = (%28x%5B1%5D%2Bx%5B2%5D%29%2F2, %28y%5B1%5D%2By%5B2%5D%29%2F2)

M = (%284%2B0%29%2F2, %281%2B%28-1%29%29%2F2)

M = (4%2F2, 0%2F2)
 
M = (2,0), that's the center of rotation.

It is not necessariy to do but one, but as a check,

If you find the midpoint of BB' using the formula

M = (%28x%5B1%5D%2Bx%5B2%5D%29%2F2, %28y%5B1%5D%2By%5B2%5D%29%2F2)

M = (%286%2B%28-2%29%29%2F2, %281%2B%28-1%29%29%2F2)

M = (4%2F2, 0%2F2)
 
M = (2,0), that gives the same center of rotation.

and

If you find the midpoint of CC' using the formula

M = (%28x%5B1%5D%2Bx%5B2%5D%29%2F2, %28y%5B1%5D%2By%5B2%5D%29%2F2)

M = (%284%2B0%29%2F2, %286%2B%28-6%29%29%2F2)

M = (4%2F2, 0%2F2)
 
M = (2,0), which also gives the same center of rotation.

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The angle of rotation is 180°, because angles APA', BPB' and CPC'
are all straight angles, or 180°.

Edwin