Question

The midpoint of is point P at (−16,6). If point A is at (−10,8), what are the coordinates of point B? (−42,20) (−22,4) (−13,7) (2,−5)

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -10}}\quad ,&{{ 8}})\quad % (c,d) B&({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{x-10}{2}~,~\cfrac{y+8}{2} \right)=\stackrel{midpoint~P}{(-16,6)}\implies \begin{cases} \cfrac{x-10}{2}=-16\\\\ x-10=-32\\ \boxed{x=-22}\\ ----------\\ \cfrac{y+8}{2}=6\\\\ y+8=12\\ \boxed{y=4} \end{cases}$

Answer 2

The correct answer is: B) (-22,4).