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The coordinate system is like a map for math. It helps us find where points are located in a space. Think of it as a way to give directions using two numbers, called coordinates. These numbers are usually in the format

• (x, y) for two-dimensional spaces

The first number, x, tells us how far left or right to go, while the second number, y, tells us how far up or down to go. This is often visualized using two lines that meet at the middle, called the axes:

• The horizontal line is called the x-axis
• The vertical line is the y-axis

In this system, any point in the space can be found by moving along these axes, making it easy to plot locations just like finding places on a map. Remember, the point where the axes intersect is a very special point, which leads us to our next topic.

The origin point is essentially the starting point or the central hub in the coordinate system. It's located where the x-axis and y-axis meet, which is at the point

• (0, 0)

This is known as the coordinates of the origin. It's like the address "0, 0" in our mathematical map. Being the central point, the origin is used as a reference for finding the position of other points.

When we talk about a point's location in the coordinate system, we often describe it in terms of its distance from the origin. Whether you move up, down, left, or right, the origin helps keep everything aligned in the coordinate grid. Understanding the origin is crucial for calculating distances in the coordinate plane.

Finding the distance from the origin to any point in the coordinate plane is a straightforward process using the distance formula. The formula is:\[d = \sqrt{x^2 + y^2}\]This formula is derived from the Pythagorean Theorem. It helps us determine how far a point

• (x, y)

is from the origin (0, 0) by calculating the straight-line distance.
To use this formula, follow these steps:

• Square the x-coordinate and the y-coordinate individually.
• Add these values together.
• Take the square root of the sum.

By applying this method, you can find the exact distance of any point from the origin, helping you compare which point is furthest away. This is especially useful in exercises where you need to determine distances between multiple points, like in the exercise presented.