Distances Between Two Point

Distance between two point in A Cartesian Plane.

1. Find the distance between two points with :

                               I.            Common y coordinates.

                            II.            Common x coordinates.

There are three ways to find the distance between two point:

     a)      By inspection

For example, in the Cartesian Plane as shown, the distance between a and b is 4 units. The distance between c and d is 3 units.

      b)      By moving one point to another

For example, in a Cartesian Plane as shown A has to move for units to reach B. therefore, the distance  between A and B is 4 units. C has to move 3 units up to reach D. therefore, the distance between C and D is 3 units.

      c)     Finding the difference between the x coordinate or y coordinate :

for example the distance between A and B

= difference between the x coordinate

= 5-1

= 4 units.

The distance between C and D

= difference between the y coordinates

= -1- (-4)

= -1 + 4

= 3 units.


d)  find the distance between two points using Pythagoras’ theorem.

The Cartesian plane shows the positions of two aircrafts, A and B. we can find the distance between the two aircrafts by drawing and appropriate right – angled triangle using AB as hypotenuse.

Hence, AB²  = AC² + CB²  

                            = 3² + 4²

                        = 25.
                        =√25

                  AB = 5 units

Thus, the distance between the aircraft is 5 units.