Find an equation for the perpendicular bisector of the line segment whose endpoints are (5,-9) and (1,3).

Given coordinates of the endpoints of a line segment  (5,-9) and (1,3).

In order to find the equation of perpendicular line, we need to find the slope between given coordinates.

Slope between (5,-9) and (1,3) is :

Slope of the perpendicular line is reciprocal and opposite in sign.

Therefore, slope of the perpendicular line = 1/3.

Now, we need to find the midpoint of the given coordinates.

Let us apply point-slope form of the linear equation:

y-y1 = m(x-x1)

y - (-3) = 1/3 (x - 3)

y +3 = 1/3 x - 1

Subtracting 3 from both sides, we get

y +3-3 = 1/3 x - 1 -3

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign