Question

The midpoint of AB is at (3,7) and A is at (0,-5). Where is B located?

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ \square }}\quad ,&{{ \square }})\quad % (c,d) &({{ \square }}\quad ,&{{ \square }}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)\qquad thus \\ ----------------------------$$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 0}}\quad ,&{{ -5}})\quad % (c,d) B&({{ \square }}\quad ,&{{ \square }}) \end{array}\qquad % coordinates of midpoint (3,7)\impliedby midpoint\qquad thus \\ \quad \\ \left(\cfrac{{{ x_2 }} + {{ 0}}}{2}=3\quad ,\quad \cfrac{{{ y_2 }} + {{( -5)}}}{2}=7 \right)\to \begin{cases} \cfrac{{{ x_2 }} + {{ 0}}}{2}=3 \\ \quad \\ \cfrac{{{ y_2 }} + {{ -5}}}{2}=7 \end{cases} \\ \quad \\ solve\ for\ x_2\ and\ y_2$