Calculating the distance between two points in a coordinate plane is a fundamental concept in mathematics. In this article, I’ll be addressing the question: What is the distance between (–8, 2.5) and (0, –4.5)? Let’s dive into the process of finding this distance and round it to the nearest hundredth.

To determine the distance between two points, we can use the formula derived from the Pythagorean theorem: d = √((x2 – x1)^2 + (y2 – y1)^2). Applying this formula to our given points (-8, 2.5) and (0, -4.5), we can calculate step by step.

Firstly, let’s find the difference in x-coordinates: x2 – x1 = 0 – (-8) = 8. Similarly, for y-coordinates: y2 – y1 = -4.5 – 2.5 = -7.

Now that we have these differences squared [(x2-x1)^2 = 64] and [(y2-y1)^2 = 49], we can proceed with adding them together: 64 + 49 =113.

Finally, taking the square root of this sum gives us √113 ≈ 10.63 as our answer for the distance rounded to the nearest hundredth.

## Calculating the Distance Formula

### Understanding the Distance Formula

When it comes to determining the distance between two points in a coordinate plane, we can rely on a reliable mathematical tool called the Distance Formula. This formula allows us to find the straight-line distance, or “as-the-crow-flies” distance, between any two given points. It’s an essential concept in geometry and has numerous practical applications.

The Distance Formula is derived from the Pythagorean theorem and works by calculating the length of a line segment connecting two points. In our case, we want to find out what is the distance between (-8, 2.5) and (0, -4.5). By plugging these values into the formula, we can determine their exact separation.

### Applying the Distance Formula to Coordinate Points

To apply the Distance Formula for our given coordinates (-8, 2.5) and (0, -4.5), we follow these steps:

- Identify and label each point’s x-coordinate and y-coordinate.
- Point A: x₁ = -8; y₁ = 2.5
- Point B: x₂ = 0; y₂ = -4.5

- Substitute these values into the formula:
- Calculate each term within parentheses:
- Square of differences in x-coordinates: = 0 – (-8) = 8
- Square of differences in y-coordinates: = -4.5 – 2.5 = -7

- Substitute the calculated values into the formula:
- Evaluate the expression within the square root:
- Simplify the expression inside the square root:

## What Is the Distance Between (-8, 2.5) and (0, -4.5)? Rounded to the Nearest Hundredth.

To round our result, √113, to the nearest hundredth, we take a look at the digit in the thousandth place (the third decimal place). Since it is greater than or equal to 5, we increase the digit in the hundredth place by one.

Therefore, rounding √113 to two decimal places gives us approximately 10.63 as our final answer for what is the distance between (-8, 2.5) and (0, -4.5).

## Understanding the Given Coordinates

Let’s delve into the given coordinates and unravel the distance between them. The coordinates in question are (-8, 2.5) and (0, -4.5). To determine the distance between these two points, we’ll employ a fundamental mathematical concept known as the distance formula.

The distance formula allows us to calculate the straight-line distance between two points in a coordinate plane. In this case, we’re working with two-dimensional Cartesian coordinates.

The formula is derived from Pythagoras’ theorem and goes as follows:

distance = √((x₂ – x₁)² + (y₂ – y₁)²)

Now let’s plug in our given values:

distance = √((0 – (-8))² + (-4.5 – 2.5)²)

Simplifying further:

distance = √(8² + (-7)²) distance = √(64 + 49) distance = √113

To round this value to the nearest hundredth, we find that it is approximately 10.63 units.

Applying the Distance Formula:

To find the distance between two points, we can use the Distance Formula. In this case, we want to determine the distance between the coordinates (-8, 2.5) and (0, -4.5). Let’s calculate it step by step.

Step 1: Identify the coordinates

The first thing we need to do is identify the coordinates of both points. Point A has coordinates (-8, 2.5), and point B has coordinates (0, -4.5).

Step 2: Plug into the formula

Now that we have our coordinates, we can plug them into the Distance Formula:

Distance = √((x₂ – x₁)² + (y₂ – y₁)²)

In our case:

Distance = √((0 – (-8))² + (-4.5 – 2.5)²)

Step 3: Simplify and calculate

Let’s simplify this equation further:

Distance = √(8² + (-7)²) Distance = √(64 + 49) Distance = √113

Step 4: Round to the nearest hundredth

Lastly, let’s round our result to the nearest hundredth as instructed.

Distance ≈ 10.63 units (rounded to two decimal places)

So, according to my calculations using the Distance Formula, the distance between (-8, 2.5) and (0,-4.5) is approximately 10.63 units when rounded to two decimal places.