Question

The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint v

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) U&({{ 3}}\quad ,&{{ 5}})\quad % (c,d) V&({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{x+3}{2}~~,~~\cfrac{y+5}{2} \right)=\stackrel{midpoint}{(5,-11)}\implies \begin{cases} \cfrac{x+3}{2}=5\\\\ x+3=10\\ \boxed{x=7}\\ ----------\\ \cfrac{y+5}{2}=-11\\\\ y+5=-22\\ \boxed{y=-27} \end{cases}$