Question

If (k,2) (2,3) and (3,4) are collinear ,than the value of k is sum

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, ΔABC is zero.

By using the area of the triangle formula

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

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

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

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

⇒ 1/2 [ - k + 1 ] = 0

⇒ - k + 1 = 0

⇒ k = 1 is the answer.