Question

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

are (-5, 1) and (-1, -5).

Answer 1

y= 2/3x +0

Explanation:

Answer 2

Given:

The endpoints of a line segment are (-5, 1) and (-1, -5).

To find:

The equation for the perpendicular bisector of the given line segment.

Solution:

The endpoints of a line segment, (-5, 1) and (-1, -5).

perpendicular bisector is perpendicular to the line segment and passes through the midpoint of the line segment.

Midpoint of the given line segment is:

`Midpoint=\left((-5+(-1))/(2),(1+(-5))/(2)\right)`

`Midpoint=\left((-5-1)/(2),(1-5)/(2)\right)`

`Midpoint=\left((-6)/(2),(-4)/(2)\right)`

`Midpoint=\left(-3,-2\right)`

The slope of the segment is:

`m=(y_2-y_1)/(x_2-x_1)`

`m=(-5-1)/(-1-(-5))`

`m=(-6)/(4)`

`m=(-3)/(2)`

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

`m* m_1=-1`

`(-3)/(2)* m_1=-1`

`m_1=(2)/(3)`

Slope of perpendicular bisector is
`m_1=(2)/(3)` and it passes through the point (-3,-2). So, the equation of the perpendicular bisector is

`y-y_1=m_1(x-x_1)`

`y-(-2)=(2)/(3)(x-(-3))`

`y+2=(2)/(3)(x+3)`

`y+2=(2)/(3)x+2`

Subtract both sides by 2.

`y=(2)/(3)x`

Therefore, the equation of the perpendicular bisector is
`y=(2)/(3)x`.