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Alenkasestr [34]
3 years ago
8

Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,1)(7,1) and (-9,9)(−9,9)

Mathematics
1 answer:
telo118 [61]3 years ago
3 0
First we are going to find the slope of these two endpoints.

Slope = \frac{Y2-Y1}{X2-X1}

Slope = \frac{9-1}{-9-7}
Slope = \frac{8}{-16}
Slope = - \frac{1}{2}

Because we need the perpendicular bisector, we do the opposite reciprocal of the slope. This is positive two. 

Your perpendicular equation begins as y = 2x + b

To find where it will bisect, we need to find the midpoint of the two endpoints. 

Midpoint = ( \frac{X1+X2}{2} ,  \frac{Y1+Y2}{2} )

Mdpt = ( \frac{7+(-9)}{2} ,  \frac{1+9}{2} )
Mdpt = ( \frac{-2}{2} ,  \frac{10}{2} )
Mdpt = (- 1, 5)

We plug this into our incomplete equation to solve for b.

5 = 2(- 1) + b
5 = - 2 + b
7 = b

Your perpendicular bisector equation is y = 2x + 7
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