Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (1,−8) and (9,2)

Answer 1

Answer: $y+3=-\frac{4}{5}(x-5)$

Step-by-step explanation:

For it to bisect the segment, we need to find the midpoint.

The midpoint is $\left(\frac{1+9}{2}, \frac{-8+2}{2} \right)=(5, -3)$

Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given segment is $\frac{-8-2}{1-9}=\frac{5}{4}$, so the slope of the perpendicular bisector is $-\frac{4}{5}$

Thus, the equation of the line in point-slope form is $\boxed{y+3=-\frac{4}{5}(x-5)}$