Easy Explanation: Which Equation Can be Used to Determine the Distance Between the Origin and (–2, –4)?

Which Equation Can be Used to Determine the Distance Between the Origin and (–2, –4)?

Have you ever wondered how to calculate the distance between two points on a coordinate plane? In this article, I’ll be addressing the question of which equation can be used to determine the distance between the origin and (-2, -4). By understanding this concept, you’ll gain valuable insights into measuring distances in a two-dimensional space.

To find the distance between two points on a coordinate plane, we can use the formula derived from Pythagoras’ theorem. This well-known equation states that in a right-angled triangle, the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides. Applying this principle to our scenario, we can consider one point as the origin (0, 0) and another point as (-2, -4).

Understanding the Distance Formula

Calculating the distance between two points can seem daunting at first, but with the right equation, it becomes a breeze. In this section, we’ll explore the distance formula and how it can be used to determine the distance between the origin (0, 0) and a specific point like (-2, -4). Let’s dive in!

The distance formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In our case, we have a right triangle formed by connecting the origin (0, 0), our starting point, and (-2, -4), our destination.

To calculate this distance using the distance formula, you’ll need to know both x- and y-coordinates of both points. The formula itself looks like this:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Let’s break it down step by step:

1. Subtracting x-coordinates: Take your second point’s x-coordinate (-2) and subtract your first point’s x-coordinate (0). This gives us (-2 – 0) = -2.
2. Squaring x-difference: Square your result from step one. In this case, (-2)^2 = 4.
3. Subtracting y-coordinates: Next up is subtracting your second point’s y-coordinate (-4) from your first point’s y-coordinate (0). This gives us (-4 – 0) = -4.
4. Squaring y-difference: Just like before, square your result from step three. In this case, (-4)^2 = 16.
5. Adding both squared differences: Add together your squared results from steps two and four. In this case, 4 + 16 = 20.
6. Taking the square root: Finally, take the square root of your sum from step five. √20 is approximately equal to 4.47.

And there you have it! The distance between the origin and (-2, -4) is approximately 4.47 units. By following these steps and using the distance formula, you can easily calculate the distance between any two points on a coordinate plane.

Exploring the Cartesian Coordinate System

In order to understand how to determine the distance between two points in a Cartesian coordinate system, let’s take a closer look at how this system works.

1. The Cartesian coordinate system, also known as the rectangular coordinate system, is named after René Descartes who introduced it in the 17th century. It provides a way to represent and locate points on a two-dimensional plane using x and y coordinates.
2. The x-axis is a horizontal line that runs left and right, while the y-axis is a vertical line that runs up and down. The point where these axes intersect is called the origin, denoted by (0, 0). Think of it as the starting point or reference point for all other points on the graph.
3. Each point on the graph can be represented by an ordered pair (x, y), where x represents its position along the x-axis and y represents its position along the y-axis. For example, (-2, -4) denotes a point that is 2 units to the left of the origin on the x-axis and 4 units below it on the y-axis.

Now that we have explored some key aspects of the Cartesian coordinate system, we can move forward with determining distance between two points. Stay tuned for our next section where we will dive into different methods and equations used for calculating distances in this system.

Remember, understanding how coordinates work within this system lays down a solid foundation for solving various mathematical problems involving distances between points. So make sure you grasp these fundamental concepts before moving on!