Question

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

Answer 1

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:

$Midpoint=\left(\dfrac{-5+(-1)}{2},\dfrac{1+(-5)}{2}\right)$

$Midpoint=\left(\dfrac{-5-1}{2},\dfrac{1-5}{2}\right)$

$Midpoint=\left(\dfrac{-6}{2},\dfrac{-4}{2}\right)$

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

The slope of the segment is:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-5-1}{-1-(-5)}$

$m=\dfrac{-6}{4}$

$m=\dfrac{-3}{2}$

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

$m\times m_1=-1$

$\dfrac{-3}{2}\times m_1=-1$

$m_1=\dfrac{2}{3}$

Slope of perpendicular bisector is $m_1=\dfrac{2}{3}$ and it passes through the point (-3,-2). So, the equation of the perpendicular bisector is

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

$y-(-2)=\dfrac{2}{3}(x-(-3))$

$y+2=\dfrac{2}{3}(x+3)$

$y+2=\dfrac{2}{3}x+2$

Subtract both sides by 2.

$y=\dfrac{2}{3}x$

Therefore, the equation of the perpendicular bisector is $y=\dfrac{2}{3}x$.

Answer 2

Answer:

y= 2/3x +0

Step-by-step explanation: