Given the endpoint

Question

Given the endpoint A (4,8) and midpoint M (-3,1), find the missing end point B. The answers are (1/2,9/2), (7/2,7/2), (-10,-6), (10,6)

Answer 1

(4,8) and (-3,1) with 1st as endpoint and 2nd as midpoint means

(-10, -6) is the other end point.

4--3 = 4+3 = 7 = the distance in x coordinates from either endpoint to the midpoint

8-1 = 7 = the distance in y coordinates from either end point to the midpoint

(that both = 7 is a coincidence, due to who ever dreamed up this problem)

subtract 7 from each coordinate in (-3,1) to get (-3-7, 1-7) = (-10, -6)

It might help to plot the points and get a close idea where the other end point should be.

(4,8) is in quadrant I

(-3, 1) is in quadrant II

The line connecting them is uphill, upward sloping. But to find the other end point, you go to quadrant III, with both x and y <0

whatever your calculations, if you don't get x<0 and y<0, you made an arithmetic mistake. third choice is the only one with both x and y < 0, so it's correct or most correct, even if you don't do any calculations.

Answer 2

The simple answer is what points are equidistant?

How far apart are 4 and -3? Seven. Seven the other direction takes us to -10.

I bet you can finish it now.