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Find the value of K if A(8, 1), B(K, -4), C(2, -5) are colline

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Find the value of K if A(8, 1), B(K, -4), C(2, -5) are collinear :

2

3

4

5

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Find the value of K if A(8, 1), B(K, -4), C(2, -5) are collinear :

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Text solutionVerified

Since the given points are collinear, they do not form a

triangle, which means area of the triangle is Zero.

Area of a triangle with vertices $(x_{1}, y_{1})$ ; $(x_{2}, y_{2})$ and $(x_{3}, y_{3})$ is $∣ ∣ \frac{x _{1} ( y _{2} - y _{3} ) + x _{2} ( y _{3} - y _{1} ) + x _{3} ( y _{1} - y _{2} )}{2} ∣ ∣$

Hence, substituting the points

(x_{1}, y_{1}) = (8, 1)

;

(x_{2}, y_{2}) = (k, - 4)

and

(x_{3}, y_{3}) = (2, - 5)

the area formula, we get

∣ ∣ \frac{8 ( - 4 + 5 ) + k ( - 5 - 1 ) + 2 ( 1 + 4 )}{2} ∣ ∣ = 0

=> 8 - 6 k + 10 = 0

=> 6 k = 18

=> k = 3

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Question Text	Find the value of K if A(8, 1), B(K, -4), C(2, -5) are collinear :
Answer Type	Text solution:1
Upvotes	150

Find the value of K if A(8, 1), B(K, -4), C(2, -5) are collinear :

Text solutionVerified

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