Given the coordinate point of one end point of Line AB and its midpoint M, find the coordiantes of the other end point.
10) B(-5,1),M(1,-1)
Hi, Bob,
It’s really not so difficult if we draw a picture to see what’s going on. Start by plotting the two points on a graph. Draw a line through the points. The “other end point” is going to be on that line, and obviously, it’s going to be the same distance away from the midpoint as the given endpoint, right? It gets real easy if we break down this distance into the “x” part and the “y” part. The “x” part is
1 - (-5) = 6 (M value minus the B value for x)
That means we moved 6 units to the right from B to M. Therefore, we have to move another 6 units to the right to get from M to A. So the x value of point A will be
1 + 6 = 7
And the “y” part is
-1 – 1 = -2 (M value minus the B value for y)
That means we moved two units down from B to M, so we have to move another two units down to get from M to A:
-1 + (-2) = -3
So point A is (7,-3).
Let’s combine all this, though, into a simpler approach. Notice that we did “M – B” then added the result to M. Well, M – B + M is simply 2M – B, so here’s the quick calc’s:
x-value of A: 2M – B = 2(1) – (-5) = 7
y-value of A: 2M – B = 2(-1) – (1) = -3
Answer: A(7,-3)
Hope that helps.
