Q:

Help me I don’t know how to solve these problems.I need to show work.

Accepted Solution

A:
I'll show you how to do the first exercises of both types, the others are identical.Find the midpoint: A=(-2,-3), B=(8,-7)The coordinates of the midpoint are the average of the correspondent coordinates, so we have[tex]M=\left(\dfrac{A_x+B_x}{2}, \dfrac{A_y+B_y}{2}\right)=\left(\dfrac{-2+8}{2}, \dfrac{-3+-7}{2}\right)=(3,-5)[/tex]Find the endpointWe simply have to reverse the previous logic: since[tex]M_x = \dfrac{A_x+B_x}{2}[/tex]we have[tex]B_x = 2M_x-A_x[/tex]and the same goes for [tex]B_y[/tex].So, we have[tex]B_x = 2\cdot 3+1=7[/tex][tex]B_y = 2\cdot 4-2=6[/tex]