Question

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

Answer 1

Answer:

answer

Step-by-step explanation:

Given : The points (K,-2), (1,4) and (-3,16)  in given order are collinear.

To find : For what the value of K?

Solution :  

When three points are collinear then the condition is  

x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) = 0

Where, x_1 = K, x_2 = 1,x_3 = -3, y_1 =-2, y_2 =4, , y_3 =16

Substituting the values,

K(4-16) + 1(16-(-2)) + (-3)(-2-4) = 0

-12k +18+18= 0

-12k + 36= 0

12k=36

k=\frac{36}{12}

k=3

Therefore, The value of k is 3.

Answer 2

Given : The points (K,-2), (1,4) and (-3,16) in given order are collinear.

To find : For what the value of K?

Solution : When three points are collinear then the condition is

$x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2) = 0$

Where, x1 = K , x2 =1 ,x3 =-3 ,y1 = -2 ,y2 =4 , y3= 16

Substituting the values,

$k(4 - 16) + 1(16 - ( - 2)) + ( - 3)( - 2 - 4) = 0$

$- 12k + 18 + 18 = 0$

$- 12k + 36 = 0$

$12k = 36$

$k = \frac{36}{12} = 3$

Therefore, The value of k is 3.