Question

Find an equation for the perpendicular bisector of the line segment whose endpoints

Answer 1

Answer:

y= -x -3

Step-by-step explanation:

A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).

Let's find the slope of the line segment.

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope of line segment

$= \frac{4 - ( - 8)}{5 - ( - 7)}$

$= \frac{4 + 8}{5 + 7}$

$= \frac{12}{12}$

= 1

The product of the slopes of 2 perpendicular lines is -1.

Let the slope of the perpendicular bisector be m.

m(1)= -1

m= -1

y= -x +c

To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.

Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.

$\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}$

Midpoint of line segment

$= ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )$

$= ( \frac{ - 2}{2} , \frac{ - 4}{2} )$

= (-1, -2)

y= -x +c

When x= -1, y= -2,

-2= -(-1) +c

-2= 1 +c

c= -2 -1

c= -3

Thus, the equation of the perpendicular bisector is y= -x -3.