Question

find the value of K , if the points (7,2),(5,1) & (3,k) are collinear​

Answer 1

Step-by-step explanation:

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) = 0x

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 =kx

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) = 07(1−k)+5(k−(−2))+3(−2−1)=0

7-7k+5k+10-6-3=07−7k+5k+10−6−3=0

-2k+8=0−2k+8=0

2k=82k=8

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

2

8

k=4k=4

Therefore, The value of k is 4.

Answer 2

Answer:

Step-by-step explanation: