Jon P. answered • 04/01/15
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Harvard honors degree in math, experienced geometry tutor
If B is the midpoint of AC, then one way to look at this is that C is as from from B and B is from A.
So to go from A to B in the x direction, you have to go from -3 to 5, which is a difference of 8. So go another 8 from B, and you get an x value of 13.
To go from A to B in the y direction, you have to go from 2 to -4, which is a difference of -6. So go another -6 from B, and you get a y value of -10.
So the answer is that C is (13, -10)
To verify this, find the midpoint between A and C. You'll see that it has the same coordinates as B.
Jon P.
tutor
The midpoint (call it xm,ym) between two points (x1,y1) and (x2,y2) is ((x1+x2)/2, (y1+y2)/2).
In other words, xm = (x1+x2)/2 and ym = (y1+y2)/2.
So in this problem you've got the midpoint (B) and one of the endpoints (A) and you're trying to find the other endpoint (C).
Take the x coordinate first: You have 5 = (-3 + x2)/2. Solve that for x2:
5 = (-3 + x2)/2
10 = -3 + x
13 = x
Then do the same for the y coordinates.
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