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Calculus: Tutoring Solution13 chapters | 111 lessons

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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.

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

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.

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.

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:

When you are at the hideout, you have moved zero footsteps in any direction. So, you are at the point (0,0). To travel to the treasure, you go 3 lines to the right and 2 lines up. You end up at the point (3,2).

The numbers on the grid simply represent distances from the origin. Positive numbers indicate moving to the right or upward. Negative numbers indicate moving to the left or downward. The point (-1,-2) tells you where you are on the map (in the middle of the ocean); however, it also tells you how far you are vertically and horizontally from the hideout - the origin.

In mathematics, an origin is a starting point on a grid. It is the point (0,0), where the *x*-axis and *y*-axis intercept. The origin is used to determine the coordinates for every other point on the graph. In a treasure map, for example, you would determine the location of your buried treasure according to its distance from your hideout - the origin.

Following this lesson, you should be able to:

- Characterize origin,
*x*-axis and*y*-axis - Explain the importance of the origin using a grid with numbering as an illustration

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16 in chapter 7 of the course:

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Calculus: Tutoring Solution13 chapters | 111 lessons

- Using Limits to Calculate the Derivative 8:11
- The Linear Properties of a Derivative 8:31
- Calculating Derivatives of Trigonometric Functions 7:20
- Calculating Derivatives of Polynomial Equations 10:25
- Calculating Derivatives of Exponential Equations 8:56
- Using the Chain Rule to Differentiate Complex Functions 9:40
- Differentiating Factored Polynomials: Product Rule and Expansion 6:44
- When to Use the Quotient Rule for Differentiation 7:54
- Understanding Higher Order Derivatives Using Graphs 7:25
- Calculating Higher Order Derivatives 9:24
- How to Find Derivatives of Implicit Functions 9:23
- How to Calculate Derivatives of Inverse Trigonometric Functions 7:48
- Applying the Rules of Differentiation to Calculate Derivatives 11:09
- Indefinite Integral: Definition, Rules & Examples 5:43
- Ordered Pair: Definition & Examples 3:57
- Origin in Math: Definition & Overview
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