## Distance Between Coordinates

 7.1 Distance Between Coordinates

 HORIZONTAL AND VERTICAL DISTANCES OF OBJECTS FROM THE ORIGIN

The diagram shows the location of a few islands. Damia and her family are on a holiday and they are staying at a resort which is located at the origin, O (0, 0). Help Damia determine the distance of each island from the origin.

• State the distance of Bahagia Island from Damia.
• Damia is at the origin (0, 0).
• Count the horizontal distance along the x-axis from the origin, 0 to 5.
• The horizontal distance of Bahagia Island from Damia is 5 units.
• The coordinates of Harmony Island are (2, 1).
• Therefore, the horizontal distance of Harmony Island from Damia is 2 units and the vertical distance is 1 unit.
• The coordinates of Sentosa Island (7,3).
• Therefore, the horizontal distance of Sentosa Island from the origin is 7 units and the vertical distance is 3 units.
 HORIZONTAL AND VERTICAL DISTANCES BETWEEN COORDINATES
 SITUATION 1

The plane below shows coordinates A and B. What are the horizontal and vertical distances from Point A to Point B?

 SITUATION 2

Coordinates for Point C, D, E, F and G are shown in the plane below. Calculate the horizontal and vertical distances between:

a) Point C and Point E
b) Point F and Point E

The horizontal distance from Point C to Point E.
4 - 1 = 3 units

The vertical distance from Point C to Point E.
3 - 2 = 1 unit

The horizontal distance from Point F to Point E.
6 - 4 = 2 units

The vertical distance from Point F to Point E.
4 - 3 = 1 unit

The distances from Point C to Point E are 3 units horizontally and 1 unit vertically.

The distance from Point F to Point E are 2 units horizontally and 1 unit vertically.