Question

In a triangle $ABC$ with vertices $A(2,3)$, $B(4,-1)$ and $C(1,2)$ Find the length of altitude, from the vertex $A$.

Answer 1

Equation of $BC$

$x=1\Rightarrow m_{BC}=\infty$

$\therefore$Slope of $AD=0$ ($m_{AD}\times m_{BC}=-1$)

Equation of $AD$

$\therefore y-3=0$ (Point slope form)

Equation of $AD$

$\therefore y=3$

Solving $BC$ and $AD$, we get co-ordinates of $D$

$\therefore D\equiv (1,3)$

$l_{BD}=\sqrt{(2-1{)}^2+(3-3{)}^2}=\sqrt{(2-1{)}^2}=1$ (Distance between two points)