SOLUTION: If M(-4, 2) is the midpoint of segment PQ and the coordinates of P are (-6,6) find the coordinates of Q.

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Question 148528: If M(-4, 2) is the midpoint of segment PQ and the coordinates of P are (-6,6) find the coordinates of Q.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Since M(-4,2)is the midpoint, this means that the midpoint coordinates are x=-4 and y=2

So the formula for the midpoint of the x-coordinate is:

%28x%5B1%5D%2Bx%5B2%5D%29%2F2=x%5Bmid%5D


%28-6%2Bx%5B2%5D%29%2F2=-4 Plug in x%5Bmid%5D=-4 and x%5B1%5D=-6 (this is from point P). Note: x%5B2%5D is the x-coordinate for the point Q


-6%2Bx%5B2%5D=-8 Multiply both sides by 2.


x%5B2%5D=-2 Add 6 to both sides.

So the x-coordinate for point Q is x=-2

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Now the formula for the midpoint of the y-coordinate is:

%28y%5B1%5D%2By%5B2%5D%29%2F2=y%5Bmid%5D


%286%2By%5B2%5D%29%2F2=2 Plug in y%5Bmid%5D=2 and y%5B1%5D=6 (this is from point P). Note: y%5B2%5D is the y-coordinate for the point Q


6%2By%5B2%5D=4 Multiply both sides by 2.


x%5B2%5D=-2 Subtract 6 from both sides.

So the y-coordinate for point Q is y=-2

So the point Q is (-2,-2)