Geo2.35

Find the equation of the altitude from A to side BC of triangle ABC formed by $A(1,1),B(-3,4),C(2,-5)\,$

Given $A(1,1),B(-3,4),C(2,-5)\,$

The equation to the line BC is $y-4=\frac{-5-4}{2-(-3)}(x+3)\,$

$5(y-4)=-9(x+3),5y+9x+7=0\,$

The slope of the BC is $\frac{-9}{5}\,$

The slope of the altitude to BC is $\frac{5}{9}\,$

The line from A with the slope $\frac{5}{9}\,$ is

$y-1=\frac{5}{9}(x-1)\,$

$9y-9=5x-5,5x-9y+4=0\,$