Question

1. # Which Expression Represents The Distance Between The Points (A, 0) And (0, 5) On A Coordinate Grid?

When it comes to math, understanding how to interpret data points on a coordinate plane is an essential skill. While the concept of plotting and finding the distance between two points may seem simple, if you’re new to this topic it can be somewhat confusing. In this article, we’ll look at one particular example: which expression represents the distance between the points (A, 0) and (0, 5) on a coordinate grid? We will discuss how to calculate this as well as some tips for understanding coordinate planes in general. So let’s get started!

## The Distance Formula

We can use the distance formula to find the distance between two points on a coordinate grid. The distance formula is:

d = |x2 – x1| + |y2 – y1|

To use the distance formula, we plug in the coordinates of the two points we are interested in finding the distance between. In this case, we want to find the distance between (A, ) and (, ), so our equation would look like this:

d = |x2 – x1| + |y2 – y1|
= |-4 – 2| + |3 – 1|
= 6

## The Coordinate Plane

The coordinate plane is a two-dimensional surface on which we can plot points, lines, and curves. The coordinate plane is divided into four quadrants by the x- and y-axes. Each quadrant is named after the coordinates of its corners: the first quadrant is Quadrant I, the second quadrant is Quadrant II, the third quadrant is Quadrant III, and the fourth quadrant is Quadrant IV.

The distance between two points on a coordinate plane can be found using the Pythagorean theorem. This theorem states that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if we know the coordinates of two points on a coordinate plane, we can use the Pythagorean theorem to find the distance between them.

We can use this theorem to find the distance between any two points on a coordinate plane, not just points with integer coordinates. For example, let’s find the distance between (-1,-1) and (2,2). We can plot these points on a coordinate grid:

(-1,-1) and (2,2) are in different quadrants, so we will need to use different formulas for each side of our triangle. For Side AB (the side from (-1,-1) to (0,0)), we will use |AB| = |b| + |a| = 1 + 1 = 2. For Side BC (the side from (0,0) to (2,2)), we will use |BC| = square root of (b^2 + c^2) = square root of (2^2 + 2^2) = square root of 8 = 2√2. Finally, for Side AC (the side from (-1,-1) to (2,2)), we will use the Pythagorean theorem: AC^2 = AB^2 + BC^2 = 4 + 8 = 12. So, the distance between (-1,-1) and (2,2) is square root of 12 = 2√3.

## The Distance Between Two Points

There are a few different ways to represent the distance between two points on a coordinate grid. The most common way is to use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In other words, if you have two points on a coordinate grid, (a, b) and (c, d), you can find the distance between them by using the following equation:

distance = √((a-c)² + (b-d)²)

Another way to find the distance between two points is to use the Manhattan distance formula. This formula is based on the fact that in a city like Manhattan, people tend to travel only in straight lines, either horizontally or vertically. So, if you have two points on a coordinate grid, (a, b) and (c, d), you can find the Manhattan distance between them by using this equation:

Manhattan distance = |a-c| + |b-d|

yet another way to calculate distances on a coordinate plane is called Chebyshev’s method. This method works well when there are obstacles in the way and you can’t travel in a straight line from one point to another. Instead, you have to travel in a zigzag pattern. To use Chebyshev’s method, find the maximum difference between any of the x-coordinates or y-coordinates of the two points. So, for example, if you have two points on a coordinate grid, (a, b) and (c, d), you can find the Chebyshev distance between them by using this equation:

Chebyshev distance = max(|a-c|, |b-d|)

## How to Find the Distance Between Two Points

There are a few different ways that you can find the distance between two points on a coordinate grid. One way is to use the distance formula, which is:

d = √((x2-x1)^2 + (y2-y1)^2)

Where d is the distance, x1 and x2 are the x-coordinates of the two points, and y1 and y2 are the y-coordinates of the two points.

Another way to find the distance between two points is to count how many units there are between the points on the grid. For example, if we wanted to find the distance between points A and B in the image above, we would count how many squares there are horizontally and vertically between the two points. In this case, there are 4 horizontal units and 3 vertical units between A and B, so the distance between them would be 7 units.

## Examples of Finding the Distance Between Two Points

There are a few different ways that you can go about finding the distance between two points on a coordinate grid. One way is to use the Pythagorean theorem, which states that in a right angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, in this case, you would take the squareroot of (A^2 + B^2). Another way to find the distance between two points is to use the Distance Formula, which is: d = √((x_2-x_1)^2 + (y_2-y_1)^2) So, in this case, you would plug in your values for x and y and solve accordingly.

## Conclusion

In conclusion, when finding the distance between two points on a coordinate grid, it is necessary to calculate the difference between each of their x and y values. In this case, we used the expression |a-0| + |b-5| which evaluated to 5. This means that the distance between (A, 0) and (0, 5) on a coordinate grid is equal to 5 units. By using this technique you should be able to quickly find distances for any set of points on a coordinate plane.

2. Have you ever been asked to work out the distance between two points on a coordinate grid? Many of us are familiar with the concept of plotting points on a graph and calculating their distance, but which expression represents this distance on a coordinate grid?

Let’s explore this question in more detail!

The distance between two points on a coordinate grid is known as the Euclidean distance. This distance is represented by the formula:

d = √(x2 – x1)2 + (y2 – y1)2

This formula is named after the mathematician Euclid, who first formulated the concept of distances between points.

Let’s say we have two points, A and B, on a coordinate grid. To calculate the distance between them, we need to know their coordinates. If point A has the coordinates (A, 0) and point B has the coordinates (0, 5), then the Euclidean distance between A and B is 5.

Therefore, in this case, the expression that represents the distance between the points (A, 0) and (0, 5) on a coordinate grid is d = √(x2 – x1)2 + (y2 – y1)2 = 5.

So, the next time you are asked to calculate the distance between two points on a coordinate grid, you’ll know exactly what to do!