Question

the equation of a perpendicular bisector
find the equation of the perpendicular bisector of the given segment by following these steps.

1. calculate the midpoint of the given segment. (0, 1)
2. determine the slope of the perpendicular line. -2/3
3. use the slope and midpoint to write the equation of the perpendicular bisector.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify point and slope

We are given the mid - point $(0,1)$ as the point on the perpendicular bisector and the slope $m =-\frac{2}{3}$ of the perpendicular bisector.

Step3: Substitute values

Substitute $x_1 = 0$, $y_1=1$ and $m =-\frac{2}{3}$ into the point - slope form:
$y - 1=-\frac{2}{3}(x - 0)$

Step4: Simplify equation

$y-1=-\frac{2}{3}x$, so $y =-\frac{2}{3}x + 1$.

Answer:

$y =-\frac{2}{3}x + 1$