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If (-3, 11), (6, 2) and (k, 4) are collinear points, then k

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If $(- 3, 11), (6, 2)$ and $($ $k$ $, 4)$ are collinear points, then $k$ is equal to

-8

-4

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(- 3, 11), (6, 2)

and

(

k

, 4)

are collinear points, then

k

is equal to

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

3

points

P (x_{1}, y_{1}), Q (x_{2}, y_{2})

and

R (x_{3}, y_{3})

are collinear, then slope

m_{PQ} =

slope

m_{QR} =

slope

m_{PR}

The given points are

P (x_{1}, y_{1}) = (3, 11), Q (x_{2}, y_{2}) = (6, 2)

and

R (x_{3}, y_{3}) = (k, 4)

Now if

3

points

P (x_{1}, y_{1}), Q (x_{2}, y_{2})

and

R (x_{3}, y_{3})

are collinear, then

slope

m_{PQ} =

slope

m_{QR} =

slope

m_{PR}

Slope

m_{PQ} = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} = \frac{4 - 11}{k - 3}

, slope

m_{PR} = \frac{y _{3} - y _{1}}{x _{3} - x _{1}} = \frac{4 - 2}{k - 6}

∴ \frac{4 - 11}{k - 3} = \frac{4 - 2}{k - 6}

\Rightarrow 2 k + 6 = - 7 k + 42

\Rightarrow k = 4

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Question Text	If $(- 3, 11), (6, 2)$ and $($ $k$ $, 4)$ are collinear points, then $k$ is equal to
Answer Type	Text solution:1
Upvotes	150

If (−3,11),(6,2) and (k,4) are collinear points, then k is equal to

Text solutionVerified

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If $(- 3, 11), (6, 2)$ and $($ $k$ $, 4)$ are collinear points, then $k$ is equal to