If the points(x,3) (9,1) and (13,2) are to be collinear,

Question

What should be the value of x?

Answer 1

Collinear points :

The points lying on the same line are called Collinear Points.

Let the points are A(x, y) = (x, 3), B(x₂, y₂) = (9, 1), and C(x₃ ,y₃) = (13, 2).

First find the line passing through the points B and C.

Slope - intercept form of the line equation is y = mx + b, where m is slope and b is y - intercept.

Slope (m) = [(y₃ - y₂)/(x₃ - x₂)]

m = [(2 - 1)/(13 - 9)]

m  = [1/4]

⇒ m = 1/4.

Now, the line BC is y = (1/4)x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (9, 1).

1 = (1/4)(9) + b

b = 1 - (9/4)

b = (4 - 9)/4

⇒ b = - 5/4.

The line BC is y = (1/4)x - (5/4).

If three points are collinear, then they are lying on the same line.

So, substitute the point A(x, y) = (x, 3) in y = (1/4)x - (5/4).

3 = (1/4)x - (5/4)

3 = (x - 5)/4

12 = x - 5

x = 12 + 5

x = 17.

Therefore, the value of x = 17.