Question

if three points ( 1-3) 1 3) (p -5 )are collineat find the values of p​

Answer 1

Let the given points be A(2, 1), B(p, - 1) and C(-1, 3).
Here, we have
x1 = 2,    y1 = 1
x2 = p,    y2 = -1
and    x3 = -1,    y3 = 3
Given three points, will be collinear if,
x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2) = 0
⇒    2(-1 - 3) + p(3 - 1) + (-1)(1 + 1) = 0
⇒    2(- 3) + p(2) + (-1 × 2) = 0
⇒    -6 + 2p - 2 = 0
⇒    2p -8 = 0
⇒    2p = 8
Hence the value of    p = 4

Answer 2

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