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

$Midpoint\ UV(5;-11)\\\\U(3;\ 5);\ V(x;\ y)\\\\\frac{x+3}{2}=5\ and\ \frac{y+5}{2}=-11\\\\x+3=10\ and\ y+5=-22\\\\x=10-3\ and\ y=-22-5\\\\x=7\ and\ y=-27\\\\Answer:V(7;-27)$

Answer 2

$Midpoint\ UV(5,-11)\\ U(3 , 5) \\\ V(x, y)\\\\Midpoint \ Formula: \\ \\ (x,y)=\left ( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right )\\\\(5,-11)=\left ( \frac{3+x }{2}, \frac{5+y }{2}\right )\\\\\frac{3+x}{2}=5\ \ | \ multiply\ both\ sides\ by\ 2 \\ \frac{5+y }{2}=-11\ \ | \ multiply\ both\ sides\ by\ 2 \\\\3+x=10\ \ |\ subtract\ 3\ to\ both\ sides \\ 5+y =-22\ \ |\ subtract\ 5\ to\ both\ sides \\\\x=10-3\\ y=-22-5\\\\x=7\\ y=-27\\\\Answer: \ V(7,-27)$