How to Find the Distance Between Two Points?

Are you curious about how to measure the distance between two points on a map or in real life? Whether you’re trying to calculate the distance between two cities or two points on a graph, it’s essential to know how to find the distance accurately. In this guide, we’ll teach you how to find the distance between two points easily.

Understanding the Coordinate Plane

Before we dive into finding the distance between two points, let’s first understand the coordinate plane. The coordinate plane is a two-dimensional surface that consists of two perpendicular number lines called the x-axis and y-axis. The point where the two lines intersect is called the origin, represented as (0,0).

Points on the coordinate plane are expressed as ordered pairs (x, y), where x represents the horizontal distance from the origin and y represents the vertical distance from the origin.

Finding the Distance Between Two Points

To find the distance between two points, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given as:

d = √((x2-x1)^2 + (y2-y1)^2)

Where:

• d is the distance between two points
• (x1, y1) and (x2, y2) are the coordinates of the two points

Let’s try to apply the distance formula to find the distance between two points on the coordinate plane. Suppose we have two points A(3, 4) and B(7, 9).

Step 1: Write down the coordinates of the two points.

A(3, 4) and B(7, 9)

Step 2: Substitute the values in the distance formula.

d = √((7-3)^2 + (9-4)^2)

Step 3: Simplify the formula.

d = √((4)^2 + (5)^2)

d = √(16 + 25)

d = √41

Therefore, the distance between points A and B is approximately 6.40 units.

Conclusion

Calculating the distance between two points is easy once you understand the coordinate plane and the distance formula. You can use this formula to find the distance between any two points on a map or graph. With practice, you’ll be able to find the distance between two points in no time!

So, now you know how to find the distance between two points, why not give it a try yourself? Start with simple examples and gradually increase the complexity. Happy learning!