Question

find the value of p for which the points (p+1 2p-2) (p-1 p) and (p-3 2p-6) are collinear

Answer 1

We are given that :-

Point A (p+1 , 2p-2)

Point B (p-1 , p)

Point C (p-3 , 2p-6)

Are co-linear

So,

ar (ABC)=0 . . . . (because area of line

is zero.)

1/2 |p+1(p-2p-6)+p-1 (2p-6-2p+2)+p-3×

(2p-2-p)| = 0

1/2 | (p+1)(6-p)+(p-1)(-4)+(p-3)(p-2)| = 0

1/2 | 6p-p-4p-2p-3p+6+6+4| = 0

1/2 | -4p+14| = 0

1/2×2 (7-2p)=0

7-2p=0

p=7/2.