We say that the distance between points A and B is the measure of the straight line connecting point A to point B. Thus, the distance between two points is a length.
This measurement can be obtained in several ways. The most common are two: measuring the line segment that connects the different points A and B using some tool that has this purpose or using a result from Analytical Geometry.
The most known instruments that are used to measure straight line segments are: ruler, measuring tape and measuring tape.
The result from Analytical Geometry, however, depends on the location of points A and B and is based on the calculation of the length of the hypotenuse of a right triangle.
Calculating the distance between two points
To calculate the distance between points A and B, we must choose points that have any coordinates A (x1y1) and B (x2y2). These coordinates represent the location of points A and B on a plane. THE distance between these two points is equal to the length of the line segment in lilac in the following image.
Example of points A and B, with their locations and coordinates in the plane
The calculation of this distance is done using the following formula:
Formula used to calculate the distance between two points
To use it, simply substitute the numerical values of the coordinates of points A and B in the places indicated in the formula and perform the calculations.
Examples
1 – Calculate the distance between points A(1,1) and B(1,4).
First, we will show through the Cartesian plane thatAB = 3. Look at the figure below:
Example of calculation between points A(1,1) and B(1,4)
Now, let's show that, using the formula for calculating the distance between two points, we will find that the distance between A and B (dAB) is equal to 3. Watch:
Calculations made from the coordinates of points A and B resulting in the distance between A and B
Example 2 – Calculate the distance between points A(– 2, 4) and B(2,2).
It is not necessary to make any drawing to calculate the distance between two points, as it is enough to have in hand the coordinates of any two points on the plane and use the formula proposed above. Watch:
Calculation used to find the distance between points A and B
By Luiz Paulo Moreira
Graduated in Mathematics
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