A Simple Calculation: Find The Distance Between (4, 2) And (-4, -4).

Finding the distance between two points on a coordinate plane can seem daunting at first, but with a simple formula, it becomes much more manageable. In this article, I’ll show you how to find the distance between the points (4, 2) and (-4, -4).

To determine the distance between these two points, we can use the distance formula derived from the Pythagorean theorem. The formula states that the square of the distance between two points is equal to the sum of the squares of their differences in x-coordinates and y-coordinates.

Applying this formula to our given points, we’ll find that the difference in x-coordinates is 8 (4-(-4)) and the difference in y-coordinates is 6 (2-(-4)). By squaring these values and adding them together, we get 100 (8^2 + 6^2).

Finally, taking the square root of this sum gives us our answer: The distance between (4, 2) and (-4, -4) is exactly √100 units. Simplified further, it’s equal to 10 units.

By following these steps and using basic algebraic calculations, we can easily find distances between any two points on a coordinate plane. So let’s dive into this problem further and explore different scenarios where finding distances might be useful!

Find The Distance Between (4, 2) And (-4, -4)

Understanding Cartesian Coordinates

Before we dive into finding the distance between two points on a plane, let’s first understand the concept of Cartesian coordinates. In a Cartesian coordinate system, points are located using an ordered pair of numbers known as coordinates. These coordinates represent the distances along the x-axis and y-axis from the origin.

In our case, we have two points: (4, 2) and (-4, -4). The first number in each pair represents the x-coordinate, while the second number represents the y-coordinate. By plotting these points on a graph, we can visualize their positions relative to each other.

The Distance Formula Explained

To find the distance between two points in a Cartesian coordinate system, we can use a formula called the distance formula. This formula is derived from applying Pythagoras’ theorem to calculate the hypotenuse of a right triangle.

The distance formula is expressed as follows:

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Here, (x₁, y₁) represents one point and (x₂, y₂) represents another point. By substituting our given values into this formula for our specific example of (4, 2) and (-4,-4), we can calculate their distance.

Calculating the X and Y Differences

To apply the distance formula correctly, we need to determine the differences in both x-coordinates and y-coordinates between our two given points.

For instance:

• The difference in x-coordinates = (-4) – 4 = -8
• The difference in y-coordinates = (-4) – 2 = -6

Now that we have determined these differences accurately for our example points of (4, 2) and (-4,-4), let’s substitute these values into the distance formula:

d = √((-8)² + (-6)²)

Simplifying this equation, we get:

d = √(64 + 36) d = √100 d = 10

Therefore, the distance between the points (4, 2) and (-4, -4) is 10 units.

By understanding Cartesian coordinates and utilizing the distance formula, we can easily find the distance between any two points on a plane.

Identifying the Given Points

To find the distance between two points, we first need to identify the coordinates of each point. In this case, we are given the following points: (4, 2) and (-4, -4). Let’s break it down step by step:

1. Point 1: (4, 2)
   • The x-coordinate of Point 1 is 4.
   • The y-coordinate of Point 1 is 2.

2. Point 2: (-4, -4)
   • The x-coordinate of Point 2 is -4.
   • The y-coordinate of Point 2 is -4.

Now that we have identified the coordinates for both points, we can proceed to calculate the distance between them.