Given the midpoint and one endpoint of a line segment, how do I find the other endpoint?

Midpoint is average of endpoints: M = (A + B) / 2, where M is midpoint and A, B endpoints.
Solve for A and get A = 2M - B.

Problem 1: other endpoint = 2 (1,-6) - (1,5) = (2,-12) - (1, 5) = (1,-17)

Problem 2: other endpoint = 2 (1,7) - (6,8) = (2,14) - (6,8) = (-4,6)

First question.
Can you point out where the (1,5) is and then where the (1,-6) is? OK, do that first, on a paper please. Put the little dots where they should be.

If midpoint is (1,-6) how many "steps" are there up to endpoint? Yes, right, 11 "STEPS"
If there are eleven "steps" from midpoint to endpoint (=top point)
then there should be eleven "steps" from midpoint "down" as well. And you will end up at - 17.

Get it?

:-)

Second question: The same principal. Try to do it on a paper and think as above and you will
solve it.

The midpoint formula is: ((x + x1)/2, (y + y1)/2) = (x2,y2).

By midpoint formula...

First Problem:

((x + 1)/2 = 1,(y + 5)/2 = -6)
(x + 1 = 2, y + 5 = -12)

Hence, the endpoint is (1, -17).

Second Problem:

((x + 6)/2 = 1, (y + 8)/2 = 7)
(x + 6 = 2, y + 8 = 14)

Therefore, the endpoint is(-4, 6).

I hope this helps!

(1,-17) is the other endpoint for the first one,

And...

(-4,6) is the other endpoint for the second one.