Question

If A (2,3),B(4,7) and c(-5,2), then find: (1) equation and (2) length of the each altitude of the ∆ABC​

Answer 1

Answer:

Given a triangle ABC with vertices A(2,3),B(4,−1),C(1,2)

Let AD be the perpendicular from the vertex A.

Now, slope of BC i.e.m1=x2−x1y2−y1=1−42−(−1)=−33=−1

Let m2 be the slope of AD.

Since, AD is perpendicular to BC.

m1m2=−1

−1m2=−1

⇒m2=1

So, slope of AD is 1.

Equation of line having one coordinate and slope is given by  

y−y1=m(x−x1)

So, equation of AD is 

y−3=1(x−2)

⇒y=x+1

⇒−x+y−1=0

We know that the perpendicular distance of a line Ax+By+C=0 from point (x1,y1) is given by