Write an equation of the perpendicular bisector of the segment with the endpoints (2,5) and (8,3)?

Answer 1

1) Determine midpoint - Use the formula

2) Determine slope between two gvien points - label it "m"

3) Determine slope of perpendicular. It is -1 / m

4) Use midpoint and slope of perpendicular in point-slope form.

Answer 2

(2,5) and (8,3) have a midpoint of (5,4) just take the average of the x coordinates (2+8)/2 = 10/2 = 5 and the average of the y coordinates (5+3)/2 = 8/2 = 4 to get (5,4)

a line through (2,5) and (8,3) have a slightly downward slope, if you plot the points and draw a line through them, or calculate it as "rise over run" difference in y coordinates divided by difference in x coordinates:

slope = (3-5)/(8-2) = -2/6 = -1/3

the perpendicular bisecting line has a negative inverse slope. change the sign and flip the fraction upside down

slope = 3 = (y-4)/(x-5)

or

y-4 = 3x -15

y = 3x -15 +4

y = 3x -11