Geometry question

Question

Given the coordinates A(-4,3), B(-5,-5) and C(3,-1). Write the equation of the perpendicular bisector of BC.

Answer 1

The perpendicular bisector goes through the midpoint of BC. The midpoint of BC is found by averaging the x values of points B and C and averaging the y values of B and C:

x value of midpoint = (-5 + 3)/2 = -2/2 = -1

y value of midpoint = (-5 + -1)/2 = -6/2 = -3

Midpoint: (-1, -3)

The slope of a perpendicular to a line is the negative reciprocal of the slope of that line.

The slope of BC is (y₂ - y₁)/(x₂ - x₁) = (-1 - -5)/(3 - -5) = 4/8 = 1/2.

The slope of the line perpendicular to that is -2

So, using the point-slope form of a line, the line that goes through (-1, -3) with a slope of -2 is:

y - -3 = -2(x - -1)

y + 3 = -2(x + 1)

If you want to put that into slope-intercept form, just multiply it out and combine like-terms:

y + 3 = -2x - 2

y = -2x - 5