Question

The midpoint of AB is M(-5, -2). If the coordinates of A are (-3, 4), what are

the coordinates of B?

Answer 1

(-7,-8)

Explanation:

From point A to the midpoint you go -2 on the x axis and -6 on the y axis. Since the definition of a midpoint says that it splits a segment into 2 equal sections, you can use the distance between point A and the midpoint to find point B. You would do (-5-2,-2-6) and that would get you (-7, -8)

Answer 2

`~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\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 +4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(-5~~,~~-2)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=-5\implies x-3=-10\implies \boxed{x=-7} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +4}{2}=-2\implies y+4=-4\implies \boxed{y=-8}`