three or much more points the lie top top a very same straight line are dubbed collinear points. Take into consideration a directly line together in the over Cartesian coordinate plane formed by x axis and y axis. This directly line together is happen through three points A, B and C whose collaborates are (2, 4), (4, 6) and (6, 8) respectively. We may additionally say, alternatively, the the 3 points A (2, 4), B (4, 6) and C (6, 8)are lying on a very same straight heat L three or more points which lie on a exact same straight heat are called collinear points.

How to uncover if three points are collinear?:

There room two techniques to uncover if three points are collinear. One is steep formula an approach and the various other is area the triangle method. Steep formula an approach to find that points room collinear. 3 or more points space collinear, if slope of any kind of two pairs of point out is same. With 3 points A, B and also C, three pairs that points deserve to be formed, lock are: AB, BC and AC. If steep of abdominal = steep of BC = slope of AC, then A, B and also C space collinear points.

You are watching: How to determine if three points are collinear

Example

Show the the 3 points A (2, 4), B (4, 6) and also C (6, 8) are collinear.

Solution:

If the 3 points A (2, 4), B (4, 6) and C (6, 8) room collinear, then slopes of any two pairs of points will certainly be equal. Now, apply slope formula to discover the slopes that the respective pairs the points: slope of abdominal = (6 – 4)/ (4 – 2) = 1, slope of BC = (8 – 6)/ (6 – 4) = 1, and also Slope that AC = (8 – 4) /(6 – 2) = 1 since slopes of any kind of two pairs the end of three pairs that points are same, this proves that A, B and C are collinear points. Area that triangle to uncover if 3 points room collinear. Three points room collinear if the value of area the triangle developed by the three points is zero. use the coordinates of the provided three point out in the area of triangle formula. If the an outcome for area is zero, climate the given points are claimed to it is in collinear. Very first of all, recall the formula for area that a triangle created by 3 points.

It is

*

In the formula above, the 2 vertical bars enclosing the variables stand for a determinant.

Let us apply the coordinates of the above three points A, B and also C in the determinant formula over for area that a triangle to inspect if the prize is zero.

See more: Where Can I Get Mint Leaves

*

Since the result for area the triangle is zero, thus A (2, 4), B (4, 6) and also C (6, 8) room collinear points.