Question

The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is ______.

विकल्प

• –2

• 2

• –1

• 1

Answer 1

The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is –2.

Explanation:

Here, x₁ = 3, x₂ = 5, x₃ = 7 and y₁ = 1, y₂ = p, y₃ = –5

If points are collinear, then area of triangle = 0

∴ `1/2 [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)] = 0`

⇒ `1/2 [3(p + 5) + 5(-5 - 1) + 7(1 - p)] = 0`

⇒ `1/2 [3p + 15 - 30 + 7 - 7p] = 0`

⇒ – 4p – 8 = 0

⇒ – 4p = 8

⇒ p = – 2