Understanding the Given Points What is the Distance Between the Points (5, 14) and (18, 3)?

I’ll help you with the introduction for your article on finding the distance between two points, (5, 14) and (18, 3). Calculating distances between points is a fundamental mathematical concept with practical applications in various fields. Using the distance formula, we can determine the precise measure of separation between these two coordinates.

To find the distance between two points on a plane, we use the Pythagorean theorem for our calculation. The formula is derived from applying this theorem to the horizontal and vertical components of the line segment connecting the two points. By squaring each component, summing them together, and then taking the square root of that sum, we arrive at a single value representing their distance apart.

 What is the Distance Between the Points (5, 14) and (18, 3)?

Introduction to the Distance Formula

When determining the distance between two points in a Cartesian coordinate system, we use a handy mathematical tool called the distance formula. This formula allows us to calculate the precise distance between any two points on a plane, and it’s an essential concept in various fields such as mathematics, physics, and computer science.

Understanding Cartesian Coordinates

Before diving into the specifics of the distance formula, let’s take a moment to understand Cartesian coordinates. In a nutshell, Cartesian coordinates provide us with a way to represent points in a plane using two perpendicular lines called axes. These axes are typically labeled as x and y, with their intersection as the origin (0, 0).

Each point on the plane can be uniquely identified by its x and y coordinates. The x-coordinate gives us information about how far horizontally the point is from the origin, while the y-coordinate tells us its vertical position relative to the origin.

Breaking Down the Given Points

To apply the distance formula effectively, we need two points for comparison. For this example, let’s consider two given points: (5, 14) and (18, 3). Now let’s break down these points:

• Point A: (5, 14)
  • x-coordinate: 5
  • y-coordinate: 14

• Point B: (18, 3)
  • x-coordinate: 18
  • y-coordinate: 3

Considering this breakdown, we can now calculate their distance using our trusty distance formula.

The H2 heading introduces “Calculating the Distance Formula,” followed by three H3 headings that delve into key aspects of understanding and applying this formula:

1. “Introduction to the Distance Formula” provides an overview of this concept.
2. “Understanding Cartesian Coordinates” explains how points are represented on a plane using Cartesian coordinates.
3. “Breaking Down the Given Points” specifically breaks down the x and y coordinates of the given points (5, 14) and (18, 3).

Calculating the Difference in x-coordinates

To understand the distance between two points, it’s important first to calculate the difference in their x-coordinates. In this case, we have two points: (5, 14) and (18, 3). The x-coordinate represents the horizontal position of a point on a graph. By subtracting the x-coordinate of one point from the other, we can determine how far apart they are along the x-axis.

Let’s take a closer look at our example:

• Point A: (5, 14)
• Point B: (18, 3)

To find the difference in their x-coordinates, we subtract the x-coordinate of Point A from that of Point B:

• Difference = 18 – 5
• Difference = 13

Therefore, there is a horizontal distance of 13 units between these two points.

Calculating the Difference in y-coordinates

Now that we have determined the difference in their x-coordinates let’s calculate the difference in their y-coordinates. The y-coordinate represents the vertical position of a point on a graph. By subtracting one y-coordinate from another, we can determine how far apart they are along the y-axis.

Using our example again:

• Point A: (5, 14)
• Point B: (18, 3)

To find the difference in their y-coordinates, we subtracted Point A’s y-coordinate from that of Point B:

• Difference = 3 – 14
• Difference = -11

The negative sign indicates that Point A is positioned below Point B along the y-axis. Therefore, there is a vertical distance of -11 units between these two points.

Given that one point has coordinates (5, 14) and another has coordinates (18, 3), we can substitute these values into our formula. By following these steps and performing calculations accordingly, we’ll obtain an accurate measurement for their spatial separation.