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If the points (-1,3), (2,p) and (5,-1) are collinear, the valu

Question

If the points $(- 1, 3), (2, p)$ and $(5, - 1)$ are collinear, the value of $p$ is

1

- 1

0

2

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Liam Discussed

If the points

(- 1, 3), (2, p)

and

(5, - 1)

are collinear, the value of

p

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Let

A (- 1, 3)

B (2, p)

and

C (5, - 1)

be the given points.

Three points are collinear if

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

Therefore,

x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) = 0 \Rightarrow - 1 (p - (- 1)) + 2 (- 1 - 3) + 5 (3 - p) = 0 \Rightarrow - 1 (p + 1) + 2 (- 4) + 5 (3 - p) = 0 \Rightarrow - p - 1 - 8 + 15 - 5 p = 0 \Rightarrow - 6 p + 6 = 0 \Rightarrow - 6 p = - 6 \Rightarrow p = 1

Hence

p = 1

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Question Text	If the points $(- 1, 3), (2, p)$ and $(5, - 1)$ are collinear, the value of $p$ is
Answer Type	Text solution:1
Upvotes	150