find the line that is the perpendicular bisector of the line segment formed by the points (1,8) and (5,-6)

Answer 1

Hi Kayleigh G

In Slope Intercept Form y = mx + b

Use the coordinates of the points given to calculate the slope m, then solve for b

Where

m=(y₂ -y₁)/(x₂ - x₁)

Then use one of the given coordinates to solve for b to get your first line

The perpendicular bisector will have an inverse slope of the opposite sign and pass through the coordinates of the midpoint of (1,8) and (5, -6)

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Midpoint = ((1+5)/2, (8+(-6))/2 = (3,1)

y=(2/7)x + 1/7

You can graph your lines to confirm that are perpendicular and the perpendicular passes through the center coordinates, at Desmos.com.

I hope this helps