How to Find the Distance Between Two Points: Step-by-Step Guide

Finding the distance between two points on a graph can be accomplished with a simple formula derived from the Pythagorean theorem. If you have two points, J (−3, 2) and K (1, −6), you can use the distance formula to determine how far apart they are.

The distance formula is expressed as:
$$ ext{Distance} = ext{√}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$
This formula is key in geometry and helps us understand how to measure distances in a coordinate plane. Let’s break down the steps using our points.

**Step 1: Identify the coordinates**
For point J, we have:
- $x_1 = -3$
- $y_1 = 2$
For point K, we have:
- $x_2 = 1$
- $y_2 = -6$

**Step 2: Calculate the differences**
Now we need to find the differences in the x-coordinates and y-coordinates:
- $x_2 - x_1 = 1 - (-3) = 1 + 3 = 4$
- $y_2 - y_1 = -6 - 2 = -8$

**Step 3: Square the differences**
Next, we square these differences:
- $(4)^2 = 16$
- $(-8)^2 = 64$

**Step 4: Add the squares**
Now add the squares together:
- $16 + 64 = 80$

**Step 5: Take the square root**
Finally, we take the square root of the total:
- Distance = √80
To simplify this, we can break 80 down:
- $80 = 16 * 5$, and since √16 = 4, we find that √80 = 4√5.

So, the distance between points J and K is **4√5**.

This formula and method can be applied to any two points on a Cartesian plane, making it a fundamental concept in geometry. Understanding how to calculate distances is not only important in math but also in real-life scenarios, such as navigation and architecture. Whether you are plotting points on a graph for a homework assignment or analyzing data in science, mastering this formula will enhance your analytical skills.

Remember to practice with different sets of points to become comfortable with the distance formula. The more you work with it, the easier it will become!