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In each of the following find the value of k, for which the po

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In each of the following find the value of $k$ , for which the points are collinear.
(i) $(7, - 2), (5, 1), (3, k)$
(ii) $(8, 1), (k, - 4), (2, - 5)$

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Sebastian Discussed

In each of the following find the value of

k

, for which the points are collinear.
(i)

(7, - 2), (5, 1), (3, k)

(ii)

(8, 1), (k, - 4), (2, - 5)

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Text solutionVerified

(i) let the given points are

A (7, - 2), B (5, 1)

and

C (3, k)

These point are collinear if area (

△ A BC

)=0

\Rightarrow x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) = 0

Here

x_{1}, y_{1}) = (7. - 2)

(x_{2}, y_{2}) = (5, 1)

(x_{3}, y_{3}) = (3, k)

\Rightarrow 7 (1 - k) + 5 (k + 2) + 3 (- 2 - 1) = 0

\Rightarrow 7 - 7 k + 5 k + 10 - 9 = 0

\Rightarrow 8 - 2 k = 0

\Rightarrow 2 k = 8

\Rightarrow k = 4

Hence the given points are collinear for

k = 4

(i) let the given points are

A (8, 1

B (k, - 4)

and

C (2, - 5)

These point are collinear if area (

△ A BC

)=0

\Rightarrow x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) = 0

Here

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

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

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

\Rightarrow 8 (- 4 + 5) + k (- 5 - 1) + 2 (1 + 4) = 0

\Rightarrow 8 - 6 k + 10 = 0

\Rightarrow - 6 k = - 18

\Rightarrow k = 3

\Rightarrow k = 4

Hence the given points are collinear for

k = 3

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Question Text	In each of the following find the value of $k$ , for which the points are collinear. (i) $(7, - 2), (5, 1), (3, k)$ (ii) $(8, 1), (k, - 4), (2, - 5)$
Answer Type	Text solution:1
Upvotes	150