Question

The end points of a line segment are (13, 1)

and (17,-7).
What is the equation of the perpendicular
bisector of this line segment?
Give your answer in the form y = mx + c,
where m and c are integers or fractions in
their simplest forms.

Answer 1

y = 2x - 41

Explanation:

`(x1 \: \: y1) = (13 \: \: \: 1) \\ (x2 \: \: y2) = (17 \: \: - 7) \\ now \\ slope = change \: in \: y \: over \: change \: in \: x \\ slope \: = y2 - y1 / x2 - x1 \\ slope = - 7 - 1 / 17 - 13 \\ - 8 / 4 \\ slope = - 2`

equation of the line

y=mx +c

`slope = y - yo \ \: over \: x - xo \\ slope = - 7 - y \: over \: 17 - x \\ 2 = - 7 - y \: over \: 17 - x`

`1( - 7 - y) = 2(17 - x) \\ - 7 - y = 34 - 2x \\ - y = 34 + 7 - 2x \\ - y = 41 - 2x \\ - y = 41 - 2x`

-y=41-2x/-y

y=2x+41