for what value of P are the points (2,1) , (P,-1) ,and (-1, 3) collinear ?
The given points will be collinear if the area of triangle formed by them is zero.
⇒ 2 (– 1 – 3) + P (3 – 1) + (– 1) (1 – (– 1)) = 0
⇒ 2 (– 4) + P × 2 – 1 × 2 = 0
⇒ – 8 + 2P – 2 = 0
⇒ 2P = 10
Hence the value of P is 5.