RedCrab Math Tutorial

# Points distance and midpoint calculation

## Introduction

Any point can be described by a pair of numbers (x, y). The numbers are the distance of A from the y axis (x), and from the x axis (y). The pair (x, y) are called the coordinates of the point A. Any points to the left of the y-axis will have a negative x coordinate. Any points below the x axis, will have a negative y coordinate.

## The distance between 2 points

Find the distance between two points A(1,2) and B(4,5).
To find the length AB we use Pythagoras’ Theorem. AB is the hypotenuse of an appropriate right-angled triangle ABC. This means that C must be the point (4,2)

The distance AC is 4 − 1 = 3
The distance BC is 5 − 2 = 3

According to Pythagoras Theorem

AB2 = AC2 + BC2

Substitute the values for AC and BC

AB2 = 32 + 32

AB2 = 9 + 9 =18

AB = √18 = 4.243

You can derive a general formula to use instead
With the RedCrab calculator use the function Distance

Distance (Point(1,2), Point(4,5)) = 4.243

## The midpoint of the line joining two points

Find the midpoint of two points A(2, 3) and B(4, 5).

Let P be the midpoint of the line segment. To find the coordinates of P the x coordinate of P must be the average of the x coordinates of A and B. The y coordinate of P must be the average of the y coordinates of A
and B.

The x coordinate is 1/2 (2 + 4) = 3. The y coordinate is 1/2 (3 + 5) = 4. So P has coordinates (3, 4)

Now we can derive a general formula for the midpoint. If the two points are A(x1, y1) and B(x2, y2) then the midpoint P must be equal to

(1/2 (x1 + x2), 1/2 (y1 + y2)

The RedCrab calculator provide the function Position to calculate any position on the line between or outside of the two points

 Points, Distance and Midpoint Distance Between Two Points Lines and Gradiants Angle Definition and Relationships Lines and Segments of Triangles Right-Triangles and Pythagorean Circle Square Rectangle Rhombus Rhomboid Trapezoid Cone Pyramid Sphere Spherical Segments and Sectors

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