Contents

- Definition
- In the Context of Mathematics, What Do “Position” and “Movement” Mean?
- What Exactly Is a Coordinate?
- What Exactly Do the Terms “Rotation,” “Translation,” and “Symmetry” Mean?
- What Is the Definition of a Position in Terms of a Vector?
- Vectors and Scalars Are Two Different Types of Mathematical Quantities
- Illustration of a Position by Vector
- The Formula for Positioning Using a Vector
- A Numerical Example of Position

# Position|Definition & Meaning

## Definition

In math, position refers to the property of an object that describes its location, often relative to some other thing. It may be qualitative (behind, above, etc.), but in most cases, it is quantified as part of a coordinate system. For example, if object A is positioned at Cartesian coordinates (5, 6) and object B at (1, 2), then object A’s position relative to B is (4, 4).

A **thing’s position** can be defined as the **amount** of space it takes up in relation to other things. In order to **describe** the **location** of one thing in **relation** to another, we can use **phrases** such as “in front,” **“behind,”** “left,” “right,” **“above,”** “below,” “top,” and **“bottom,” among** others.

In the **following** figure, the **position** of a **parallelogram** is right to the **circle.**

## In the Context of Mathematics, What Do “Position” and “Movement” Mean?

In the context of **mathematics, “position”** refers to the process of **determining** and noting where **something** is situated, **typically** on a grid or a map. In most cases, your **youngster** will complete this task using **coordinates.** The ideas of rotation, **translation,** and **symmetry** are **included** under the umbrella term **“movement.”**

In geometry, **sometimes known** as the **study** of shapes, **issues** such as **movement** and **position** are both covered.

## What Exactly Is a Coordinate?

The **location** of such a **point** on such a grid can be determined with the help of **something** called **coordinates.** A **coordinate** is indeed a pair of numbers that are **distinguished** by a comma and **enclosed** in brackets.

For **example,** a coordinate would look **like** this: (7, 8). The **numbers** that make up a coordinate provide you with information about how far you need to travel along either axis of a grid in order to locate the **point.**

By telling yourself to move **“all** along the corridor but also up the stairs,” you can help yourself remember that you should first move all along the bottom axis (X) to find the very first number of a coordinate and then start moving up the axis (Y) to find the 2nd number of a coordinate.

**You** can do this by using the phrase “all **along** the **corridor** but also up the stairs.” To locate the **point** indicated by the **coordinates** (4, 2), **move four** spaces down the axis that **runs horizontally** across the **bottom** of the grid, and **afterward,** move two **spaces vertically** along the axis that **runs horizontally** across the top of the grid.

## What Exactly Do the Terms “Rotation,” “Translation,” and “Symmetry” Mean?

The **technique** of **spinning** as well as turning a form, is **referred** to as **rotation.** The form rotates **360 degrees** while maintaining its **appearance** and size during the process.

Moving a shape along a **grid either** up, **down, left,** or **right** is **called** translation. The **shape** does not **rotate** or alter its outward appearance or its size; **rather,** it merely moves in one or even more directions.

**Reflection** is the key to **understanding** symmetry. If **you** are able to draw a line across the **middle** of a **shape** and each half is indeed a **mirror** image to the other, then the shape is said to have **symmetry.**

## What Is the Definition of a Position in Terms of a Vector?

A **position vector** is indeed a **straight** line that is used to **define** the **location** of a **moving** point in relation to a **body.** One **end** of the line is **attached** to the body, while the **other** end of the line is attached to the **moving** point. When the point **moves,** its position vector will **undergo** a change in either its **length, **its direction, or both, **depending** on the nature of the **movement.**

It is **possible** to define a **position vector** as a vector that **represents** either the **position** or even the **location** of a **particular** point with **respect** to an **arbitrary reference** point such as the origin. **Always moving** in the direction of a certain **location,** the **direction** of a **position** vector **points** in the **direction** of a vector’s origin.

## Vectors and Scalars Are Two Different Types of Mathematical Quantities

When **determining position,** the **direction** that one **faces** is quite **essential.** When you **claim** that you are **located** at positive 6 meters in the **x-direction,** what you are **actually indicating** is that you are **located** 3 meters towards the right of a y-axis. This points in a **certain direction.**

A **number** that takes into account **direction** is **referred** to as a vector. A scalar is a **number** that may be written in **either** direction without **affecting** its value.

Scalars include things like **temperature,** for instance. **Because** there is no clear path that it follows. Even if it may be 70 **degrees Fahrenheit** outside, the temperature inside the **building** is not 70 **degrees** Fahrenheit. It could be 40 degrees Celsius, but it will never be 40 degrees **Celsius** when you head west. Not at all how things work with temperature. The **temperature** is an **example** of a scalar.

**Because** the **direction** is important, the position is **represented** as a vector. However, **distance** is **indeed** a scalar variable. The length of your **journey** can be measured in **distance.** For instance, if you **sprint** around your **room** while keeping the axis on the **ground,** you might run a **fairly** long way, all the way up to a total distance of fifty meters.

However, your location is not **fifty** meters away. For example, your position could be described as having a minus **3-meter** value just on the **x-axis** and a plus **4-meter** value on the y-axis. The distance you traveled did not change **regardless** of the direction in which you ran; you still covered fifty meters.

**Therefore,** while considering the **distance, orientation** is **irrelevant.** The **measure** of **distance** is indeed a scalar.

## Illustration of a Position by Vector

In **most** situations, a **position vector** of such an item is **calculated** by starting from the origin. **Imagine** that an item is placed within space in the **following** manner.

## The Formula for Positioning Using a Vector

Before we can **calculate** a **position** vector of any point in the xy plane, we need to have the **point’s** coordinates in front of us.

Take into consideration points A and B, each of which has the coordinates (w1, **x1)** and (w2, **x2),** accordingly. In order to calculate a **position** vector, we must first take the respective components of A and subtract them from the **components** of B in the **following** manner:

AB = (w2 – w1)*i + (x2 – x1)*j

Point A **serves** as the **starting** point for the position vector AB, which continues on to point B.

## A Numerical Example of Position

**Which** of these **figures** lies **beneath** the **Circle?**

### Solution

**From** the **previous** knowledge of **position,** the **triangle** is beneath the **circle.**

*All mathematical drawings and images were created with GeoGebra.*