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Find the value(s) of k for which the points (3k-1,k-2),(k,k-7)

Question

Find the value(s) of $k$ for which the points $(3 k - 1, k - 2), (k, k - 7)$ and $(k - 1, - k - 2)$ are collinear.

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Asher Discussed

Find the value(s) of

k

for which the points

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

and

(k - 1, - k - 2)

are collinear.

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Given,

A (3 k - 1, k - 2), B (k, k - 7) an d C (k - 1, - k - 2)

Two points are said to be collinear if their slopes are equal

\Rightarrow

Slope of

A B

=

Slope of

BC

We have,

$\Rightarrow$ Slope between two points $= (\frac{y _{2} - y _{1}}{x _{2} - x _{1}})$

\Rightarrow

\frac{k - 7 - k + 2}{k - 3 k + 1} = \frac{- k - 2 - k + 7}{k - 1 - k}

\Rightarrow

\frac{- 5}{- 2 k + 1} = \frac{- 2 k + 5}{- 1}

\Rightarrow

(5 - 2 k) (1 - 2 k) = 5

\Rightarrow

5 - 10 k - 2 k + 4 k^{2} = 5

\Rightarrow

4 k^{2} - 12 k = 0

\Rightarrow

4 k (k - 3) = 0

\Rightarrow

k = 0, 3

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Question Text	Find the value(s) of $k$ for which the points $(3 k - 1, k - 2), (k, k - 7)$ and $(k - 1, - k - 2)$ are collinear.
Answer Type	Text solution:1
Upvotes	150