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

1 answer:

8 0

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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V1 = l · w · h (l - length, w - width, h - height)
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V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
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GarryVolchara [31]

X = Maggie's age

y = The brother's age

x + y = 42

y = 3x - 6

Using the substitution property, we can replace y in the first equation with the 3x - 6 in the second equation like so:

x + (3x - 6) = 42

Then solve this equation for x like so:

x + (3x - 6) = 42

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