Question

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y) midpoint(-23,10) endpoint (-17,7)

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -17}}\quad ,&{{ 7}})\quad % (c,d) &({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{x-17}{2}~,~\cfrac{y+7}{2} \right)=\stackrel{\textit{midpoint}}{(-23,10)}\implies \begin{cases} \cfrac{x-17}{2}=-23\\\\ x-17=-46\\ \boxed{x=-29}\\ ----------\\ \cfrac{y+7}{2}=10\\\\ y+7=20\\ \boxed{y=13} \end{cases}$