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**Anemori** Points A(0,8), B(12, -8), C(-12,-8)

Slope of AB is $\displaystyle - \frac {4}{3} $

Slope of BC is is 0

Slope of AC is $\displaystyle \frac {4}{3} $

Perpindicular formula:

$\displaystyle m2= -\frac {1}{m1} $

m1 and m2 must not be = 0

Finding the perpindicular of $\displaystyle y= - \frac {4}{3}\color{red}x \color{black}+ b$ to point (-12, -8)

Let m1 = $\displaystyle - \frac {4}{3} $

$\displaystyle m2 = - \frac {1}{-\frac {4}{3}} = \frac {3}{4}$

Solve for b

Let (x,y) = (12, -8)

$\displaystyle -8 = -\frac {3}{4}(12) + b $

$\displaystyle -8 = \color{red}-\color{black}(9) + b $

Subtract both sides:

$\displaystyle 1 = b $

Equation:

$\displaystyle y = -\frac {3}{4}x + 1 $

Now for $\displaystyle y = \frac {3}{4}x + b $and (-12, -8)

is $\displaystyle y = \frac {3}{4}x + 1 $

What else I need to do to get the Orthocenter of the triangle?