Question

If the points (7, - 2),(5,1),(3,k) are collinear, then find the value of k.

Answer 1

see the attachment. here is your answer

Answer 2

Answer:

The value of k is 4.  

Step-by-step explanation:

Given : If the points A( 7,-2), B (5,1) and C (3,k) are collinear.

To find : 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, $x_1 = 7, x_2 = 5, x_3 = 3, y_1 =-2, y_2 = 1, y_3 =k$

Substituting the values,

$7(1-k) +5(k-(-2)) +3(-2-1) = 0$

$7-7k+5k+10-6-3=0$

$-2k+8=0$

$2k=8$

$k=\frac{8}{2}$

$k=4$

Therefore, The value of k is 4.