Question

the points (p,2),(-3,4) and (-7,1) are collinear then find the value of P

Answer 1

If the 3 points are collinear then the area formed by the triangle of the given points shall be 0
A(p,2)    B(-3,4)   C(-7,1)

So, Area of ABC =1/2 [x1 (y2 - y3) + x2(y3 - y1) + x3 (y1 - y2)] = 0

substituting the values,

=> 1/2{p (2) -3 (-1) -7 (-2)} =0

=> 2p +3 +14 =0
=> 2p = -17
=> p =-17/2

Answer 2

If 3 points are collinear then Ιx₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)Ι=0
x₁=p,y₁=2,x₂=-3,y₂=4,x₃=-7,y₃=1.
Ιp(4-1)+(-3)(1-2)+(-7)(2-4)Ι=0
Ι3p+3+14Ι=0
3p=-17
p=-17/3

Hope this helps you ............... :)