# If the Points a (2,3), B (4,K ) and C (6,-3) Are Collinear, Find the Value of K. - Mathematics

If the points  A (2,3),  B (4,k ) and C (6,-3) are collinear, find the value of k.

#### Solution

The given points are A (2,3),  B (4,k ) and C (6,-3)

Here , (x_1 = 2 , y_1 =3) , (x_2 =4, y_2 =k) and (x_3 = 6, y_3=-3)

It is given that the points A, B and C are collinear. Then,

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

⇒ 2 (k+3) + 4 (-3-3) + 6 (3-k) = 0

⇒ 2k + 6 - 24 +18 -6k =0

⇒ - 4k = 0

⇒ k =0

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 17