Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (-11,-20) endpoint (-2,-14) The other endpoint is ____

Answer 1

$\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)$

$\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}$