Question

Can someone help me please

Answer 1

The vector that goes from A to the midpoint AB shall be called v.

Now, do you see that if we take v and place it at AB, we will end up at B?

So that will give us a way to do all the calculations

v = AB - A = (-2,4) - (3,-2) =(-2-3, 4-(-2)) = (-5,6)

So then

B = AB + v = (-2,4) + (-5,6) = (-7,10)

Answer 2

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