Question

Find the equations to the sides of the triangles the coordinates of whose angular points are respectively
$(1,4),(2,-3)$, and $(-1,-2)$.

Answer 1

Equation of $AB$

$y-4=\left(\frac{-3-4}{2-1}\right)(x-1)y-4=-7(x-1)y-4=-7x+7y+7x=11$

Equation of $BC$

$y-(-3)=\left(\frac{-2-(-3)}{-1-2}\right)(x-2)y+3=-\frac{1}{3}(x-2)3y+9=-x+23y+x+7=0$

Equation of $AC$

$y-4=\left(\frac{-2-4}{-1-1}\right)(x-(-2\left)\right)y-4=3(x+2)y-4=3x+6y-3x=10$