The value of p for which the points (-1, 3), (2, p) and (5, -1) are collinear is

Formula used:

Area of a triangle:

Let coordinates be A(x1, y1), B(x2, y2) and C(x3, y3),

then the area of a triangle is given as,

Δ =  \(\frac{1}{2}\)[x1 ( y2 -  y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y2 )]

Note: If the point A, B, C are collinear then 

The area of Δ ABC should be equal to zero.

Calculation:

Given that,

(-1, 3), (2, p) and (5, -1) are collinear.

⇒ Area of Δ ABC = 0

∵ Δ =  \(\frac{1}{2}\)[x1 ( y2 -  y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y2 )]

⇒ \(\frac{1}{2}\)[-1{p - (-1)} + 2(-1 - 3) + {5(3 - p)] = 0

⇒ -p - 1 + 2 × (-4) + 15 - 5p = 0

⇒ -6p + 6 = 0

⇒ p = 1