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Origin in Math: Definition & Overview

Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

The origin is more than just the (0,0) point on a graph. It is the starting point from which all other points are measured. Read this lesson to learn about how the origin is used in mathematics.

Definition

The banana you had for lunch probably originated in Costa Rica. The bus you took to school may have originated at a bus station. An origin is a beginning or starting point, and, in mathematics, the origin can also be thought of as a starting point. The coordinates for every other point are based on how far that point is from the origin. At the origin, both x and y are equal to zero, and the x-axis and the y-axis intersect.

Cartesian Plane with origin labeled

Example

Imagine that you are a pirate and have buried your loot on a small island in the Pacific. Being one of those careful pirates who thinks ahead, you create a map so that you can find the treasure again later.

Island with X for treasure

This map isn't very useful, of course, if it doesn't give you any idea of the distance or direction to the treasure from some other useful place, like your hideout.

So, in order to keep track of where the treasure is buried relative to your hideout you create a grid on your map.

Same map with grid
Same island with grid overlayed

Each line on the grid represents 100 steps. By counting lines between the big X and your hideout (the triangle), you know how far to travel in both the up/down and right/left directions. You find that your hideout and the treasure are three blue lines (300 steps) apart in the right/left direction. Your hideout and the treasure are also two green lines (200 steps) apart in the up/down direction. Of course, you would probably really travel diagonally straight between the two places, but it is much easier to describe the directions and distances by pretending the travel would happen along the lines on the grid.

Now, it would be much easier to describe travel between the hideout and the treasure if you numbered the green and blue lines. It would also be easier if you chose one of the two locations as the starting point. For example, you might choose the hideout as the starting point, or origin. That way, you can say, 'Go three lines (or 300 feet) to the right.' Your directions to your fellow pirates would become much clearer. In this case, it doesn't really matter if you call the hideout the starting point (or originating point or origin) and describe travel to the treasure, or vice versa. It is simply important that you are clear and consistent. If the hideout is the origin, the map looks like this:

Same map with grid and numbering
Same island with grid and numbering added

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