# Mastering The Distance Formula: What Is The Distance Between (–13, 9) And (11, 2) On A Coordinate Grid?

The distance between two points on a coordinate grid can be determined using the Pythagorean theorem. In this case, we are trying to find the distance between the points (-13, 9) and (11, 2). To calculate this distance, we need to find the difference in both the x-coordinates and y-coordinates of the two points.

First, let’s find the difference in x-coordinates: 11 – (-13) = 24

Next, let’s find the difference in y-coordinates: 2 – 9 = -7

Now that we have our differences, we can use them to calculate the distance using the Pythagorean theorem formula:

Distance = √[(difference in x)^2 + (difference in y)^2]

Plugging in our values:

Distance = √[(24)^2 + (-7)^2]

Simplifying further:

Distance = √[576 + 49] Distance = √625 Distance = 25

Therefore, the distance between (-13, 9) and (11, 2) on a coordinate grid is 25 units.

## What Is The Distance Between (–13, 9) And (11, 2) On A Coordinate Grid?

So, you’re wondering about the distance between two points on a coordinate grid? Well, buckle up because we’re about to dive into the exciting world of calculating distances!

To find the distance between two points on a coordinate grid, we can use a nifty little formula called the distance formula. This formula allows us to determine the straight-line distance between any two points in a Cartesian plane.

Let’s take your example: (–13, 9) and (11, 2). To calculate the distance between these two points, we’ll follow these steps:

1. Identify the coordinates of each point: In this case, our first point is (-13, 9) and our second point is (11, 2).
2. Plug the values into the distance formula: The distance formula looks like this:
d = √((x₂ – x₁)² + (y₂ – y₁)²)
Substituting our coordinates into this equation:
d = √((11 – (-13))² + (2 – 9)²)
3. Simplify and compute: Let’s do some math!
d = √(24² + (-7)²)
d = √(576 + 49)
d = √625
4. Calculate the square root of 625:
d ≈ √625
d ≈ 25

There you have it! The approximate distance between (–13, 9) and (11, 2) on a coordinate grid is approximately 25 units.

Remember that the units used for measuring distances will depend on how your coordinate grid is scaled. It could be inches, centimeters, or any other unit of measurement.

Calculating distances using the distance formula can be incredibly useful in various fields such as navigation, physics, and engineering. It allows us to determine the shortest path between two points on a plane.

## Understanding The Coordinate Grid System

Navigating the coordinate grid system is essential for determining distances between points. Let’s explore this system to better understand how we can calculate the distance between two points, such as (-13, 9) and (11, 2).

The coordinate grid system consists of a horizontal x-axis and a vertical y-axis intersecting at the origin point (0,0). Each point on the grid is represented by an ordered pair in the form (x, y), where x represents the position along the x-axis and y represents the position along the y-axis.

To calculate the distance between two points on a coordinate grid, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, with sides of lengths a and b and hypotenuse of length c, c^2 = a^2 + b^2. In our case, we can consider each axis as one side of a right-angled triangle and find the hypotenuse as our desired distance.

Let’s apply this concept to find out what is the distance between (-13, 9) and (11, 2). We’ll start by finding the difference in x-coordinates:

11 – (-13) = 24

Then we’ll find the difference in y-coordinates:

2 – 9 = -7

Now that we have these differences, we can create another set of coordinates representing these differences: (24,-7). This new point represents a right-angled triangle on our coordinate grid.

Using these coordinates as sides of our triangle, we can apply Pythagoras’ theorem:

c^2 = 24^2 + (-7)^2 c^2 = 576 + 49 c^2 = 625 c ≈ √625 c ≈ 25

Hence, applying Pythagoras’ theorem tells us that there is a distance of approximately 25 units between the points (-13, 9) and (11, 2) on the coordinate grid.

Understanding how to navigate the coordinate grid system and apply mathematical concepts like the Pythagorean theorem allows us to calculate distances accurately. By utilizing these tools, we can explore various points on the grid and determine their relationships in terms of distance and position.