Question

if the points (0, 2), (k, -1), (2, 0) are collinear, then k =​

Answer 1

Answer:

Step-by-step explanation:

Let givegivenpoints

A ( x1, y1 ) = ( 0, 2 ),B (x2, y2 ) = ( k, - 1 ) and C ( x3, y3 ) = ( 2, 0 )

We know the area of ΔAΔABC

1/2 | x1 ( y2 - y3 ) + x2 (y3 - y1 ) + x3 ( y1 - y2 ) | = 0 (∵The given points are collinear )

⇒ 1/2 | 0 (- 1 - 0 ) + k ( 0 - 2 ) + 2 ( 2 + 1 ) | = 0

⇒ 1/2 | 0 ( - 1 ) + k ( - 2 ) + 2 ( 3 ) | = 0

⇒ 1/2 | 0 - 2k + 6 | = 0

⇒ 1/2 | -2k + 6 | = 0

⇒ - 2k + 6 = 0

⇒ 2k = 6

⇒ k = 6/2

⇒ k = 3 is the answer.