Question

Find the value of 'p' for which the points (-1,3) , (2,p) and (5,-1) are collinear.

Answer 1

three point colinear means form triangle by three points is zero .
use this concept
A (-1,3) B (2, p) and D (5,-1)
ar (ABC)=1/2{(-1)(p+1)+2 (-1-3) +5 (3-p)}
=> 0 =1/2 {-p-1-8+15-5p}
=>-6p+6=0
=> p=1

Answer 2

area of triangle = 0
1/2 [ -1 ( p +1) + 2 ( - 1 - 3) + 5 ( 3 - p)] = 0
=> -p - 1 - 8 + 15 - 5p = 0
=> - 6p + 6 = 0
=> - 6p = - 6
=> p = - 1