Question

find the value of p for which the points (-1 3),(2,p), and (5,-1) are collinear​

Answer 1

Answer:

.............value of p is 1...........

Answer 2

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✔️ Given that A(-1,3) , B(2,p) and C(5,-1) are collinear .

So we know that if three points A, B and C are Collinear then distance of AB = CB .

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Distance of AB

$ab \: = \sqrt{( {2 + 1)}^{2} + ( {p - 3)}^{2} }$

Distance of CB

$cb \: = \sqrt{( {5 - 2)}^{2} + ( {1 + p)}^{2} }$

Now , If AB = CB then :-

$\sqrt{( {3)}^{2} + {p}^{2} + ( {3)}^{2} - 6p} = \sqrt{( {3)}^{2} + 1 + {p}^{2} + 2p }$

By squaring both sides we will remove the roots .

→ 9 + p² +9 - 6p = 9 +1 +p² +2p

→ 18 - 10 = 8p

→ 8 = 8p

→ 1. = p

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So value of p is 1