Question

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

Answer 1

A perpendicular bisector cuts a line segment in half at a 90-degree angle.

To find the perpendicular bisector, find the midpoint of the lines and the negative reciprocal. Finally, Plug these into the equation for a line in slope-intercept form.

(3,-1) = (x1,y1)

(-3,5) = (x2,y2)

Apply midpoint formula

`midpoint=\text{ (}(x1+x2)/(2),(y2+y1)/(2))\text{ = }(3-3)/(2),(-1+5)/(2)=(0,2)`

find the slope (m)

`m=(y2-y1)/(x2-x1)=(5-(-1))/(-3-3)=(6)/(-6)=-1`

Negative reciprocal of the slope:

-1 =1

Slope intercept form:

y=mx+b

Where:

m= slope

b= y-intercept

Put the negative reciprocal of the slope in the equation:

y= 1x+b

y=x+b

Plug the points of the midpoint into the line, and solve for b

Midpoint (0,2)

2=0+b

2=b

Final equation:

y= x+2