Respuesta :
The equation is [tex]y = \frac{3}{2} x - \frac{11}{2}[/tex]
Explanation:
We have to first find the mid-point of the segment, the formula for which is
[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )[/tex]
So, the midpoint will be [tex](\frac{-1+7}{2} , \frac{1-5}{2} )\\\\[/tex]
= [tex](3,-2)[/tex]
It is the point at which the segment will be bisected.
Since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope is [tex]\frac{-5-1}{7+1}[/tex] = [tex]-\frac{2}{3}[/tex]
Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of [tex]-\frac{2}{3}[/tex] is [tex]\frac{3}{2}[/tex]
To write an equation, substitute the values in y = mx + c
WHere,
y = -1
x = 3
m = 3/2
Solving for c:
[tex]-1 = \frac{3}{2} X 3 + c\\\\-1 = \frac{9}{2}+c\\ \\c = \frac{-2-9}{2} \\\\c = \frac{-11}{2}[/tex]
Thus, the equation becomes:
[tex]y = \frac{3}{2} x - \frac{11}{2}[/tex]
