Question

For what value of K (k,11) (1,5) (-1,1) are collinear

Answer 1

For collinear points their slopes should be equal Therefore 5-11/1-k should be equal to 1-5/-1-1 Therefore -6/1-k = 2 -6 = 2-2k -8 = -2k K = 4

Answer 2

Let, A=(k,11)=(x1, y1)
B=(1,5)=(x2, y2)
C=(-1,1)=(x3, y3)
Slope of line AB = Slope of line BC
y2-y1. y3-y2
-------- = ---------
x2-x1. x3-x2

5-11. 1-5
------- = --------
1-k. -1-1

-6. -4
------ = -----
1-k. -2

-6.
------ = 2
1-k.
After this Cross Multiply,

2(1-k)= -6
2-2k= -6
-2k= -6-2
-2k= -8
k= -8
----
-2
K= 4.

Therefore, the value of K is 4.