geometry problem.?

Question

use triangle RES with coordinates r(0,0), e(4,-6) and S (8,4) to find the equation of the perpendicular bisector of side RE.

Answer 1

Use triangle RES with coordinates R(0,0), E(4,-6) and S(8,4) to find the equation of the perpendicular bisector of side RE.

Find the slope of the line RE

m = ∆y/∆x = (0 + 6)/(0 - 4) = 6/-4

The slope of the perpendicular bisector is the negative reciprocal of that.

m' = -1/m = 2/3

Find the midpoint of R and E.

M = [(0+4)/2, (0-6)/2] = M(2, -3)

Write the equation of the perpendicular bisector.

y + 3 = (2/3)(x - 2)
y = (2/3)x - 4/3 - 3
y = (2/3)x - 13/3

Answer 2

The coordinates of the midpoint of RE: (2, -3)
The slope of the bisector: -(4-0)/(-6-0) = 2/3, -change of x/change of y
The equation is: y + 3 = (2/3)(x-2), point-slope form