Question

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

Find the slope of HI.
Find the perpendicular slope.
Use that slope and G in the point slope formula: y-y1=m(x-x1).
Rewrite the equation so x and y are on one side and the constant is on the other.

Answer 1

Finding the slope of HI (
`m`):


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

Finding the perpendicular slope (
`m'`):


`m\cdot m'=-1\iff (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}`