Question

2. If Q(-5, 1) is the midpoint of PR and R is located

at (-2.-4), what are the coordinates of P?

Answer 1

The answer is (-8,6)

Answer 2

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ P(\stackrel{x_1}{x}~,~\stackrel{y_1}{y})\qquad R(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +x}{2}~~~ ,~~~ \cfrac{ -4 +y}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE Q} }{(-5~~,~~1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -2 +x }{2}=-5\implies -2+x=-10\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ -4 +y }{2}=1\implies -4+y=2\implies \boxed{y=6}`