Question

Find the value of k if points (k, 3), (6, - 2) and (-3, 4) are collinear.

Answer 1

Answer:

(-5/6-k)=6/-9

-5/6-k=-2/3

15=12-2k

2k=-3

K=-3/2

Answer 2

k = -3/2

Step-by-step explanation:

3 points are collinear if the area of the triangle formed by the 3 vertices is zero.

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

Given vertices are:  (k, 3), (6, - 2) and (-3, 4)  

 (1/2) [k (-2 - 4 )+ 6 (4 - 3) - 3 (3 + 2] = 0  

  1/2 [k(-6) +6(1) -3(5)] = 0

  /2 (-6k-9)

   6k = -9

 Therefore k = -3/2