Question

If (8,1) and (K-4) and (2,-5) are collinear then find K​

Answer 1

Answer:

value of k is 3

Step-by-step explanation:

if three points are collinear, then the area of the  triangle formed by joining these three points is 0

let the three points (8,1) , (K-4) and (2,-5) be A , B ,  and C respectively

then area of triangle ABC = 0

here ,

x₁ = 8

x₂ = k

x₃ = 2

y₁ = 1

y₂ = - 4

y₃ = - 5

area of triangle = 1/2 [ x₁ ( y₂ - y₃ ] + x₂ ( y₃ - y₁ ) + x₃ ( y₁ - y₂ ) ]

= 1/2 [ 8 ( - 4 - { - 5 } ) + k ( - 5 - 1 ) + 2 ( 1 - { -4 } ) ]

but area of this triangle is 0

so 1/2 [ 8 ( - 4 - { - 5 } ) + k ( - 5 - 1 ) + 2 ( 1 - { - 4 } ) ] = 0

=> 1/2 [ 8 ( - 4 + 5 ) + k ( - 5 - 1 ) + 2 ( 1 + 4) ] = 0

=> 1/2 [ 8 ( 1 ) + k ( - 6 ) + 2 ( 5) ] = 0

=> 1/2 [ 8 - 6 k + 10 ] = 0

=> 8 - 6 k + 10 = 0

=> 6 k = 8 + 10

=> 6 k = 18

=> k = 18/6 = 3

so value of k is 3