Question

The value of p, for which the points A(3,1), B(5,p) and C(7,-5) are collinear, is
(a) -2
(b) 2
(d) 1
(c) -1​

Answer 1

Answer:

option (a) is correct

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Answer 2

The required "option a) - 2" is correct.

Step-by-step explanation:

The given points are A(3, 1), B(5, p) and C(7, - 5).

Here, $(x_{1} =3,y_{1} =1)$, $(x_{2} =5,y_{2} =p)$ and $(x_{3} =7,y_{3} =-5)$

To find, the value of p = ?

The given points A,B and C are collinear.

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

⇒ 3(p - (- 5)) + 5(- 5 - 1) + 7(1 - p) = 0

⇒ 3(p + 5) + 5(- 6) + 7(1 - p) = 0

⇒ 3p + 15 - 30 + 7 - 7p = 0

⇒ - 4p + 22 - 30  = 0

⇒ - 4p - 8 = 0

⇒ 4p = - 8

⇒ p = $\dfrac{-8}{4} =-2$

∴ p = - 2

Thus, the required "option a) - 2" is correct.