Question

How do you find the coordinates of the other endpoint of a segment with the given midpoint is (5,-11) and the other end point is (3,5)?

Answer 1

Other end point: `color(red)(""(7,-27))`

Explanation:

If `(x_m,y_m)` is the mid-point between `(x_1,y_1)` and `(x_2,y_2)`
then
`color(white)("XXX")(x_2-x_m)=(x_m-x_1)color(white)("xxx")rarr color(white)("xxx")x_2=x_m+(x_m-x_1)`
and
`color(white)("XXX")(y_2-y_m)=(y_m-y_1))color(white)("xxx")rarr color(white)("xxx")y_2=y_m+(x_m-y_1)`

In this case
`color(white)("XXX")(x_m-x_1)=5-3=2color(white)("xxxxxxxx")rarr color(white)("xxx")x_2=5+2=7`
and
`color(white)("XXX")(y_m-y_1)=-11-5=-16color(white)("xx")rarr color(white)("xxx")y_2=-11+(-16)=-27`