The coordinates of the 2 given points are W(-5, 2), and X(5, -4).
First, we find the midpoint M using the midpoint formula:
[tex]\displaystyle{ M_{WX}= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )= (\frac{-5+5}{2}, \frac{2+(-4)}{2} )=(0, -1).[/tex]
Nex, we find the slope of the line containing M, perpendicular to WX. We know that if m and n are the slopes of 2 parallel lines, then mn=-1.
The slope of WX is [tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{2-(-4)}{-5-5}= \frac{6}{-10}= -\frac{3}{5} [/tex].
Thus, the slope n of the perpendicular line is [tex]\displaystyle{ \frac{5}{3} [/tex].
The equation of the line with slope [tex]\displaystyle{ n= \frac{5}{3} [/tex] containing the point M(0, -1) is given by:
[tex]\displaystyle{ y-(-1)=\frac{5}{3}(x-0)[/tex]
[tex]\displaystyle{ y+1= \frac{5}{3}x[/tex]
[tex]\displaystyle{ 3y+3=5x[/tex]
[tex]\displaystyle{ 5x-3y-3=0 [/tex]
Answer: 5x-3y-3=0
