Question

point (-5, 1), (1, P) & (4-2)
are collinear if the value of p
is
​

Answer 1

Answer:

ans will ne p = -1

as it is given in image

Answer 2

Given:

We have given three points,

A  ( -5, 1 )     (x₁, y₁ )

B  ( 1, p )     ( x₂ y₂ )

C  ( 4, -2 )    ( x₃ y₃ )

To Find:

Value of P?

Solution:

We know that if three points are collinear then the area of the triangle formed by this triangle will be zero.

Area of triangle= $\frac{1}{2}$ × [ x₁ ( y₂ – y₃ ) + x₂ ( y₃ – y₁ ) + x₃( y₁ – y₂ ) ]

so,

area of traingle will be zero.

Put the values of x and y in the above equation and equate to zero.

0 =  $\frac{1}{2}$ × [ -5 ( p – (-2) ) + 1 ( -2 – 1 ) + 4 ( 1 – p ) ]

0 = $\frac{1}{2}$ × [  -5 ( p +2 ) + 1 ( -3 ) + 4 ( 1 - p ) ]

0 = $\frac{1}{2}$ × [ -5p - 10 + (-3)+ 4 - 4p ]

0  -9 p - 9

9p = -9

p = -1

Hence the value of p is -1.