The distance between two points on a coordinate grid can be determined using a formula called the distance formula. In this particular case, we are calculating the distance between the points (7, 8) and (-8, 0). To find this distance, I’ll use the following formula:

𝑑 = √((𝑥2 – 𝑥1)^2 + (𝑦2 – 𝑦1)^2)

Substituting the coordinates of our points into the formula, we get:

𝑑 = √((-8 – 7)^2 + (0 – 8)^2)

Simplifying further:

𝑑 = √((-15)^2 + (-8)^2)

Calculating:

𝑑 = √(225 + 64)

Finally:

𝑑 = √289

Therefore, the distance between the points (7, 8) and (-8, 0) on a coordinate grid is 17 units.

## Understanding Coordinate Grids

### Calculating the Distance Between Two Points on a Coordinate Grid

When working with a coordinate grid, it’s essential to understand how to calculate the distance between two given points. This distance can be determined using the Pythagorean theorem or by applying the distance formula. Let’s break down each method to gain a better understanding.

To calculate the distance between two points (x₁, y₁) and (x₂, y₂), we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In our case, we consider each axis as one side of this triangle.

Using these differences as our triangle’s legs, we can apply the Pythagorean theorem:

a² + b² = c²

where ‘a’ represents one leg length (horizontal difference), ‘b’ represents another leg length (vertical difference), and ‘c’ represents our desired hypotenuse/distance.

Plugging in our values:

15² + 8² = c² 225 + 64 = c² 289 = c²

Taking the square root of both sides gives us:

√289 = √c² 17 = c

Therefore, the distance between points A(7, 8) and B(-8, 0) on a coordinate grid is **17 units**.

### Using the Pythagorean Theorem to Find the Length of the Hypotenuse

The Pythagorean theorem is a fundamental concept that helps us determine unknown lengths in a right triangle. By utilizing this theorem, we can calculate distances between two points on a coordinate grid.

In our example, we used point A(7, 8) and point B(-8, 0) to find the distance between them. We identified the differences in their x and y coordinates as our triangle’s legs and applied the Pythagorean theorem to solve for the hypotenuse.

Remember, when applying this theorem to a coordinate grid, always consider each axis as one side of your right triangle. This method allows you to find precise distances without having to rely solely on visual estimation.

### Applying the Distance Formula to Solve for the Distance

Another approach for calculating the distance between two points on a coordinate grid is by using the distance formula. The formula provides a straightforward way of determining precise distances without needing visualization or geometric concepts like triangles.

The distance formula states:

d = √((x₂ – x₁)² + (y₂ – y₁)²)

Using our previous example with points A(7, 8) and B(-8, 0), let’s apply this formula:

d = √((-8 – 7)² + (0 – 8)²) = √((-15)² + (-8)²) = √(225 + 64) = √289 = 17

Once again, we arrive at **17 units** as our calculated distance between points A and B using the distance formula.

## What Is The Distance Between the Points (7, 8) and (–8, 0) on a Coordinate Grid?

Let’s dive into plotting the points (7, 8) and (-8, 0) on a coordinate grid. Visualizing these points helps us understand their positions relative to one another and calculate the distance between them.

To plot a point on a coordinate grid, we follow two simple steps:

- Locate the x-coordinate: In our example, for the point (7, 8), we move horizontally along the x-axis until we reach the value of 7.
- Locate the y-coordinate: Once we’re at x = 7, we move vertically along the y-axis until we reach the value of 8.

After following these steps for both points, we can mark them on our coordinate grid. The first point (7, 8) will be slightly to the right and above the origin (0, 0). The second point (-8, 0) will be significantly to the left of the origin but still aligned with it horizontally.