Question

The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is

• A. 6
• B. 1
• C. 4
• D. 8

Answer 1

The correct option is B

1

The given points A(-1, 3), B(2, p), C(5, -1) are collinear.

⇒ Area ΔABC formed by these points should be zero.

⇒ The area of ΔABC = 0

⇒ $\frac{1}{2}$( $x_1$( $y_2$- $y_3$) + $x_2$( $y_3$- $y_1$) + $x_3$( $y_1$ - $y_2$)) = 0

⇒ -1(p + 1) + 2 (-1 - 3) + 5(3 -p) = 0

⇒ -p - 1 - 8 + 15 - 5p = 0

⇒ -6p +15 - 9 = 0 ⇒ -6p = -6 ⇒ p = 1

Hence the value of p is 1.