Question

write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3, - 1) and (3,5). the use of the grid below is optional

Explanation:

Step1: Find the mid - point of the line segment

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=3,y_1 = - 1,x_2=3,y_2 = 5$. So the mid - point is $(\frac{3 + 3}{2},\frac{-1+5}{2})=(3,2)$.

Step2: Determine the slope of the line segment

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we get $m=\frac{5-(-1)}{3 - 3}=\frac{6}{0}$, which means the line segment is vertical.

Step3: Find the slope of the perpendicular bisector

Since the line segment is vertical, the perpendicular bisector is horizontal. The slope of a horizontal line is $m = 0$.

Step4: Write the equation of the line

The equation of a line in point - slope form is $y - y_1=m(x - x_1)$. Using the mid - point $(3,2)$ and $m = 0$, we have $y-2=0(x - 3)$, which simplifies to $y=2$.

Answer:

$y = 2$