Finding the distance between two points

In this publication, we will consider what the distance between two points is, and by what formula it is calculated (on the plane and in space). We will also analyze examples of solving problems on this topic.

Calculating the distance between two points

Distance between two points is the length of the segment (d) that you get when you combine them.

If the points A (x_ay_a) и B (x_by_b) located on a plane, then the distance between them is calculated by the formula:

If the points A (x_ay_a, of_a) и B (x_by_b, of_b) are in XNUMXD space, the distance is calculated as follows:

Examples of tasks

Task 1

Two points are given on the plane: A (2, 5) и B (-3, 7). Let’s find the distance between them.

Decision:

Let’s use the first formula above:

Task 2

Find the distance between points A (-1, 0, 12) и B (2, 6, -4).

Decision:

We apply the corresponding formula, substituting the known values ​​into it: