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)?

1 Answer
Aug 16, 2017

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#