ime the Vave ol p dor which

1.	ime the Vave ol p dor which
Answer» Given , Points = ( p+1 , 2p-2 ), ( p-1 , p) and (p-3 , 2p-6) For the given points ( x₁ , y₁ ) , ( x₂ , y₂ ) and ( x₃ , y₃) to be collinear then [ x₁ ( y₂ - y₃ ) + x₂( y₃ - y₁ )+ x₃( y₁- y₂ )] = 0 Here, x₁ = p + 1 y₁ = 2p - 2 x₂ = p - 1 y₂ = p x₃ = p - 3 y₃ = 2p - 6 Substituting the values in the formula , ( p + 1 ) ( p - ( 2p - 6 ) ) + ( p - 1 ) ( 2p - 6 - ( 2p - 2 ) ) + ( p - 3 ) ( 2p - 2 - ( p ) ) = 0 ( p + 1 ) ( p - 2p + 6 ) ) + ( p - 1 ) ( 2p - 6 - 2p + 2 ) ) + ( p - 3 ) ( 2p - 2 - p ) = 0 ( p + 1 ) ( -p + 6 ) + ( p - 1 ) ( -4 ) + ( p - 3 ) ( p - 2 ) = 0 - p² - p + 6p + 6 - 4p + 4 + p² - 3p - 2p + 6 = 0 - 4p + 16 = 0 4p = 16 Dividing both the sides by 4 4p / 4 = 16 / 4 p = 4 Hence, For the points to be collinear , p = 4

Answer»

Given ,

Points = ( p+1 , 2p-2 ), ( p-1 , p) and (p-3 , 2p-6)

For the given points ( x₁ , y₁ ) , ( x₂ , y₂ ) and ( x₃ , y₃) to be collinear then

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

Here,

x₁ = p + 1 y₁ = 2p - 2

x₂ = p - 1 y₂ = p

x₃ = p - 3 y₃ = 2p - 6

Substituting the values in the formula ,

( p + 1 ) ( p - ( 2p - 6 ) ) + ( p - 1 ) ( 2p - 6 - ( 2p - 2 ) ) + ( p - 3 ) ( 2p - 2 - ( p ) ) = 0

( p + 1 ) ( p - 2p + 6 ) ) + ( p - 1 ) ( 2p - 6 - 2p + 2 ) ) + ( p - 3 ) ( 2p - 2 - p ) = 0

( p + 1 ) ( -p + 6 ) + ( p - 1 ) ( -4 ) + ( p - 3 ) ( p - 2 ) = 0

- p² - p + 6p + 6 - 4p + 4 + p² - 3p - 2p + 6 = 0

- 4p + 16 = 0

4p = 16

Dividing both the sides by 4

4p / 4 = 16 / 4

p = 4

Hence,

For the points to be collinear , p = 4

Discussion