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Find the value of k if points (k,3), (6,-2) and (-3,4) are c

Question

Find the value of $k$ if points $(k, 3), (6, - 2) an d (- 3, 4)$ are collinear.

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Levi Discussed

Find the value of

k

if points

(k, 3), (6, - 2) an d (- 3, 4)

are collinear.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

(k,3),(6,-2),(-3,4) are

collinear

here

x_{1} = k, y_{1} = 3

x_{2} = 6, y_{2} = - 2

x_{3} = - 3, y_{3} = 4

So, as given that the points are collinear, then,

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

k (- 2 - 4) + 6 (4 - 3) + 3 (3 + 2) = 0

k (- 6) + 6 (1) + (- 3) \times 5 = 0

- 6 k + 6 - 15 = 0

- 6 k - 9 = 0

k = \frac{9}{6} = \frac{3}{2}

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Question Text	Find the value of $k$ if points $(k, 3), (6, - 2) an d (- 3, 4)$ are collinear.
Answer Type	Text solution:1
Upvotes	150