### Home > PC > Chapter 1 > Lesson 1.2.2 > Problem1-81

1-81.

Find the perpendicular bisector of the segment $\overline {AB}$ for $A\left(2, 9\right)$ and $B\left(8, −3\right)$.

Find the slope of the line.

Find the midpoint of the line.

Find the slope of the perpendicular line.

Use the point slope form of a line substituting one of the known points and your perpendicular slope.

$m=\frac{9-(-3)}{2-8}=\frac{12}{-6}=-2$

$\left ( \frac{8 + 2}{2}, \frac{9 + (-3)}{2} \right ) \left ( \frac{10}{2}, \frac{6}{2} \right ) = (5,3)$

It is the negative reciprocal of the slope of the line:

$\frac{1}{2}$

$y-3=\frac{1}{2}(\text{x}-5)$