Question

Help me with Geometry

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) P&({{ 3}}\quad ,&{{ 5}})\quad % (c,d) Q&({{ c}}\quad ,&{{ d}}) \end{array}\quad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)=(-2,0)\\\\ -----------------------------\\\\ \left(\cfrac{{{ c}} + {{ 3}}}{2}\quad ,\quad \cfrac{{{ d}} + {{ 5}}}{2} \right)=(-2,0)M\implies \begin{cases} \cfrac{c+3}{2}=-2\\\\ \cfrac{d+5}{2}=0 \end{cases}$

if you solve those equations for "c" and "d" respectively, you'd get, well the Q point of c,d