SOLUTION: If M(-5,2)is the midpoint of segment PQ and the coordinates of P are (-6,8) find the coordinates of Q. Select the correct answer.

Algebra ->  Graphs -> SOLUTION: If M(-5,2)is the midpoint of segment PQ and the coordinates of P are (-6,8) find the coordinates of Q. Select the correct answer.       Log On


   

Question 148520: If M(-5,2)is the midpoint of segment PQ and the coordinates of P are (-6,8) find the coordinates of Q. Select the correct answer.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If M(-5,2)is the midpoint of segment PQ and the coordinates of P are (-6,8) find the coordinates of Q. Select the correct answer.



Since M(-5,2)is the midpoint, this means that the midpoint coordinates are x=-5 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=-5 Plug in x%5Bmid%5D=-5 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=-10 Multiply both sides by 2.


x%5B2%5D=-4 Add 6 to both sides.

So the x-coordinate for point Q is x=-4

------------


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

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


%288%2By%5B2%5D%29%2F2=2 Plug in y%5Bmid%5D=2 and y%5B1%5D=8 (this is from point P). Note: y%5B2%5D is the y-coordinate for the point Q


8%2By%5B2%5D=4 Multiply both sides by 2.


x%5B2%5D=-4 Subtract 8 from both sides.

So the y-coordinate for point Q is y=-4

So the point Q is (-4,-4)