Question

Find the area of triangle formed by the points(P+1,1),(2P++1,3)

Answer 1

Let A= (p+1, 1), B= (2p+1, 3), C = (2p+2, 2p)

If the points A, B and C are collinear the slope of AB = slope of AC

(3–1)/{(2p+1)-(p+1)} = (2p-3)/{(2p+2)-(2p+1)} or 2/p = (2p-3)/1

So 2p^2 -3p -2 = 0

Solving we get p=2 or -1/2.