Question

If a segment has an endpoint at (3, 2) and the midpoint at (-1, 2), what are the coordinates of the other endpoint?

Answer 1

Midpoint between the points (x1,y1) and (x2,y2) is $( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )$

so if mid is (-1,2) and an endpoint is (3,2) then
mid between (3,2) and (x2,y2) is $( \frac{3+x_2}{2},\frac{2+y_2}{2} )$

the x values and y values corespond

(3+x2)/2=-1
times 2
3+x2=-2
minus 3
x2=-5


other one
(2+y2)/2=2
times 2
2+y2=4
minus 2
y2=2

the other point is (-5,2)

Answer 2

The other endpoint would have to be (-5,2), going off the definition of a midpoint. Since 3 is for units to the right of -1, that would mean that the other end point would have to be 4 units to the left, which is -5.