To find the distance between two points on a graph using the Pythagorean Theorem, follow these simple steps. It's easy once you practice a bit!

Step-by-Step Guide:

1. Identify the Points: First, you need two points. Let's say we have point A and point B. For example, A(1, 2) and B(4, 6).

2. Calculate the Differences: Next, figure out the differences in their x-coordinates and y-coordinates:

   • For x: $\Delta x = x_2 - x_1 = 4 - 1 = 3$
   • For y: $\Delta y = y_2 - y_1 = 6 - 2 = 4$

3. Set Up the Equation: Now, we can make a right triangle. The sides of the triangle are $|\Delta x|$ and $|\Delta y|$. Use the Pythagorean Theorem: $c^2 = (\Delta x)^2 + (\Delta y)^2$ Plugging in our numbers, we get: $c^2 = (3)^2 + (4)^2 = 9 + 16 = 25$

4. Solve for the Distance: Finally, to find the distance $c$, take the square root: $c = \sqrt{25} = 5$

So, the distance between points A(1, 2) and B(4, 6) is 5 units.

Practice Problems:

Try these on your own:

1. Find the distance between C(2, 3) and D(5, 7).
2. Calculate the distance between E(-1, -1) and F(2, 2).

Using the Pythagorean Theorem like this is not only a fun math trick, but it’s also an important skill in geometry. You’ll see it again as you continue with math!