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Coordinate Geometry

Let us consider the following graph.

In the above figure, O is the origin, A is a point at a distance of 3 units on x-axis, and B is a point at a distance of 4 units on y-axis.

Can we find the distance between the two points A and B?

We shall find this out in the given video, where first we will see the basic approach and then work out a formula to calculate the distance between any two points.

Now, that we have seen how to use the distance formula, let’s understand the derivation of the distance formula with the help of the video given below.

In coordinate geometry, the distance formula has a lot of applications. Let us look at one of its applications.

What can you say about the three points (–6, 10), (–1, 1), and (3, –8)? Are they collinear?

Let us see.

If the sum of the distances of any point from the other two is equal to the distance between the other two points, then we can say that the given points are collinear.

For example, let (–6, 10), (–1, 1), and (3, –8) be denoted by A, B, and C respectively.

Now, using distance formula,, we obtain

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