Find the value of p for which the points (5, 1), (1, p) and (4, -2) ar

1.	Find the value of p for which the points (5, 1), (1, p) and (4, -2) arecollinear.
Answer» x₁ = -5 x₂ = 1x₃ = 4 y₁ = 1y₂ = py₃ = -2 For the points to be collinear :- x₁(y₂ -y₃) + x₂(y₃ - y₂) + x₃(y₁ - y₂) = 0 -5{ p -(-2)} + 1 ( - 2 - 1) + 4( 1 - p) = 0 -5(p+2) + 1(-3) + 4( 1 - p) = 0 -5p - 10 - 3 + 4 - 4p = 0 -9p - 9 = 0 -9p = 9 p = 9/-9 p = -1

Find the value of p for which the points (5, 1), (1, p) and (4, -2) arecollinear.

Answer»

x₁ = -5 x₂ = 1x₃ = 4

y₁ = 1y₂ = py₃ = -2

For the points to be collinear :-

x₁(y₂ -y₃) + x₂(y₃ - y₂) + x₃(y₁ - y₂) = 0

-5{ p -(-2)} + 1 ( - 2 - 1) + 4( 1 - p) = 0

-5(p+2) + 1(-3) + 4( 1 - p) = 0

-5p - 10 - 3 + 4 - 4p = 0

-9p - 9 = 0

-9p = 9

p = 9/-9

p = -1