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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.

Verified Answer :

arthurpdc

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:

\(\boxed{y+3x=9}\)

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