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

Explanation

Slope of `BC` is `m_(1)=(2-(-1))/(1-4)=-1`
Slope of its perpendicular line `AM` is
`m_(2)=-(1)/(m_(1))=1`
Equation of `AM` is,
`y-3=1(x-2)`
`implies x-y+1=0`
Equations of `BC` is ,
`y+1=-1(x-4)`
`implies y+1=-x+4`
`impliesx+y-3=0`
Length of perpendicular form `A(2,3)` to `BC`
`=|(2+3-3)/(sqrt(1+1))=sqrt(2)` unts