Question

17. For what value of k, the points (k, -2), (1, 4) and (-3, 16) in given order are collinear​

Answer 1

Answer:

Step-by-step explanation:

If A (x1, y1) , B ( x2, y2 ) and C ( x3, y3 ) are lying on a line.

Then ,they can't form a triangle. i.e,area of ΔABC is zero.

By using, area of the triangle formula

Δ = 1/2 [ x1 (y2 - y3 ) + x2 ( y3 - y1 ) + x3 ( y1 - y3 ) ] = 0

⇒ 1/2 [ k ( 4 - 16 ) + 1 ( 16 - (- 2) ) + ( - 3 ) ( - 2 - 4 ) ] = 0

⇒ 1/2 [ k ( - 12 ) + 1 ( 16 + 2 ) + ( - 3 ) ( - 6 ) ] = 0

⇒ 1/2 [ - 12k + 18 + 18 ] = 0 ( ∵ + × - = - ; - × - = + )

⇒ 1/2 [ - 12k + 36 ] = 0

⇒ 1/2 × 12 [ - k + 3 ] = 0

⇒ 6 [ - k + 3 ] = 0

⇒ - k + 3 = 0

⇒ k = 3 is the answer.