Question

Y is the midpoint of XZ .X has coordinates (2, 4), and Y has coordinates (-1, 1). Find the coordinates of z.

Answer 1

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) X&({{ 2}}\quad ,&{{ 4}})\quad % (c,d) Z&({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{x+2}{2}~,~\cfrac{y+4}{2} \right)=\stackrel{Y}{(-1,1)}\implies \begin{cases} \cfrac{x+2}{2}=-1\\\\ x+2=-2\\ \boxed{x=-4}\\ ------\\ \cfrac{y+4}{2}=1\\\\ y+4=2\\ \boxed{y=-2} \end{cases}$