Question

g the equation of a perpendicular bisector
find the equation of the perpendicular bisector of the given segment by following these steps.
√1. determine the slope of the given segment. 3/2 √
√2. calculate the mid - point of the given segment. (0,1) √

1. determine the slope of the perpendicular line. 2/3

-2/3
2/3
3/2
check

Explanation:

Step1: Recall slope - perpendicular relationship

If the slope of a line is $m_1$ and the slope of a perpendicular line is $m_2$, then $m_1\times m_2=- 1$. Given the slope of the given segment $m_1 = \frac{3}{2}$.

Step2: Calculate the perpendicular slope

We solve the equation $\frac{3}{2}\times m_2=-1$ for $m_2$. Cross - multiply to get $3m_2=-2$, then $m_2 =-\frac{2}{3}$.

Answer:

$-\frac{2}{3}$