Collinear points definition and examples

Have you heard about collinear points? What does the meaning of collinear points? Now let us learn the definition of collinear points and also we will try to learn this concept perfectly by examples.

Basically, in coordinate geometry chapter, we are going to get this concept.

Definition of collinear points:

The points which are lying on the same line are called collinear points.

From the above diagram, we can clearly observe that the points A, P, R, S and T lies on the same line so they are called as collinear points.

Conditions to check whether the given points are collinear or not:

We can check collinearity of points based on distance formula. If P, Q and R be the three points then the point’s are said to be collinear if PQ + QR = PR.

Based on area of the triangle also we can check collinearity of points. If the area of the triangle is  0 then we can say that the given points are collinear.

By using slope formula also we can check collinearity of points. If P, Q and R be the three points and if the slope of PQ is equal to the slope of QR then we can say that the points P, Q and R are collinear.

Examples :

*Check whether the points (2, 5) (24, 7) and (12, 4) are collinear or not?

Solution:

We can check collinearity of points in three ways. Now for this problem let us use one of them. Am using slope formula to solve this problem.

Let the point be A (2, 5), B (24, 7) and C (12, 4).

As slope of AB = slope of BC. We can say that the given points A (2, 5), B (24, 7) and C (12, 4) are collinear.

*If the points P (8, 1), Q (15, 7) and R (x, 3) are collinear then find x.

Solution:

As the points P, Q and R are collinear

Slope of PQ = slope of QR

6 (x-15) = -4 x 7

6x – 90 = -28

6x = -28 + 90

6x = 62

x = $\frac { 62 }{ 6 }$