Question

USING the Midpoint Formula , POINT A is at (-3,-5) and point M is at (-0.5,0). what are the coordinates of point B

Answer 1

`\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-5})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{x-3}{2}~~,~~\cfrac{y-5}{2} \right)~~=~~\stackrel{\stackrel{Midpoint}{M}}{(-0.5~,~0)}\implies \begin{cases} \cfrac{x-3}{2}=-0.5\\[1em] x-3=-1\\ \boxed{x= 2}\\ \cline{1-1} \cfrac{y-5}{2}=0\\[1em] y-5=0\\ \boxed{y=5} \end{cases}`