Question

Write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3,-1) and (-3, 5).

Answer 1

First, we neeed to find the mid-point

The formula for calculating the midpoint is given by:

`(x_m,y_m)=((x_1+x_2)/(2),\text{ }(y_1+y_2)/(2)_{})`

From the points given

(3,-1) and (-3, 5).​

x₁ = 3 y₁=-1 x₂=-3 y₂=5

substitute the values into the formula

`(x_m,y_m)=((3-3)/(2),\text{ }(5-1)/(2))`

Evaluate

`(x_m,y_m)=(0\text{ , 2)}`

Next, we need to find the slope;

The formula for finding slope is given by;

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

`m=(5+1)/(-3-3)`
`m=(6)/(-6)\text{ = -1}`

slope of perpendicular lines is given by;

`m_1m_2=\text{ -1}`

where m₂ is the new slope

-1m₂ = -1

m₂ = 1

Next, is to find the intercept of the new line

To do that, simply substitute m=1 x=0 and y=2 into y=mx+ b and then solve for b

That is;

2= 1(0) + b

2 = b

b= 2

To form the new equation, simply substitute m=1 and b=2 into y=mx+b

That is;

y = 1(x) + 2

y= x+ 2

Hence; the equation of the line that is a perpendicular bisector is;

y = x + 2