Question

Given GHI G(4,-3), H(-4,2), and I(2,4), find the perpendicular bisector of HI in standard form.

Answer 1

Finding the slope of HI ($m$):

$m=\dfrac{\Delta y}{\Delta x}\iff m=\dfrac{y_I-y_H}{x_I-x_H}=\dfrac{4-2}{2-(-4)}\iff m=\dfrac{2}{6}\iff\\\\\boxed{m=\dfrac{1}{3}}$

Finding the perpendicular slope ($m'$):

$m\cdot m'=-1\iff \dfrac{1}{3}m'=-1\iff\boxed{m'=-3}$

Using the formula:

$y-y_G=m'(x-x_G)\iff y-(-3)=-3(x-4)\iff\\\\ y+3=-3x+12\iff y=-3x+9$

Rewriting:

$\boxed{y+3x=9}$