Question

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

Answer 1

Answer:

Step-by-step explanation:

Here we have x1 = 2, x2 = 4, y 1 = 3, y2 = k, x3 = 6, y3 = -3.

Given that the three points are collinear.

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

= > 2(k + 3) + 4(-3 - 3) + 6(3 - k) = 0

= > 2k + 6 + 4(-6) + 18 - 6k = 0

= > 2k + 6 - 24 + 18 - 6k = 0

= > -4k + 0 = 0

= > -4k = 0

= > k = 0.

Therefore the value of k = 0

Hope this helps!

Answer 2

Answer: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 = 2, x_2 = 4, y_1 = 3, y_2 = k, x_3 = 6, y_3 = -3

Substituting the values,

2(k + 3) + 4(-3 - 3) + 6(3 - k) = 0

2k + 6 + 4(-6) + 18 - 6k = 0

2k + 6 - 24 + 18 - 6k = 0

-4k + 0 = 0

k=0

Therefore, The value of k is 0.

Step-by-step explanation: