SOLUTION: A half-turn centered at (−3,4) is applied to (−5,1). Find coordinates for the image point. What are the coordinates when the half-turn centered at (a, b) is applied to (x, y)?

Question 1164197: A half-turn centered at (−3,4) is applied to (−5,1). Find coordinates for the image point. What are the coordinates when the half-turn centered at (a, b) is applied to (x, y)?

Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

A half turn centered about A, applied to B, results in an image C where A is the midpoint of BC.

For the general case (your second question), a half turn centered at (a,b) applied to (x,y) will produce an image at (a+(a-x),b+(b-y)), or (2a-x,2b-y).

To get some learning from this problem, it would be good to solve the first of your problems in two different ways, to see that the answers are the same: (1) by using the idea of (-3,4) as the midpoint of the line segment; and (2) by using the general formula.

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