Question

In the triangle ABC with vertices A$(2,3)$, B$(4-1)$ and C $(1,2)$, find the equation and length of attitude from the vertex A

Answer 1

Given triangle ABC

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

Slope of $BC=\frac{2-(-1)}{1-4}=\frac{3}{-3}=-1$

Slope of AD$=1$

Equation AD$=y-3=1(x-2)$

$y-3=k-2$

$=x-y+1=0$ ………….$\left(1\right)$

Equation BC $y-2=-1(k-1)$

$y-2=-x+1$

$x+y-3=0$ ………..$\left(2\right)$

$\left(1\right)+\left(2\right)\Rightarrow 2x-2=0\Rightarrow x=1$

$1-y+1=0$

$\Rightarrow y=2$

$D(1,2)$

Equation pf AD $x-y+1=0$

Length of attitude $=\sqrt{(2-1{)}^2+(3-2{)}^2}$

$=\sqrt{2}$.