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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.

User NoelProf
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1 Answer

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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}
User Yati Sagade
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