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.
Equation of BC
x=1⇒mBC=∞
∴Slope of AD=0 (mAD×mBC=−1)
Equation of AD
∴y−3=0 (Point slope form)
Equation of AD
∴y=3
Solving BC and AD, we get co-ordinates of D
∴D≡(1,3)
lBD=√(2−1)2+(3−3)2=√(2−1)2=1 (Distance between two points)