What is the distance between the points (0, 0) and (3, 4)?

The distance between the points (0, 0) and (3, 4) is 5 units.

To find the distance between two points on a coordinate plane, we use the distance formula, which is derived from Pythagoras' theorem. The distance formula is:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

In this case, the points given are (0, 0) and (3, 4). Here, \( x_1 = 0 \), \( y_1 = 0 \), \( x_2 = 3 \), and \( y_2 = 4 \). Plugging these values into the formula, we get:

\[ \text{Distance} = \sqrt{(3 - 0)^2 + (4 - 0)^2} \]
\[ \text{Distance} = \sqrt{3^2 + 4^2} \]
\[ \text{Distance} = \sqrt{9 + 16} \]
\[ \text{Distance} = \sqrt{25} \]
\[ \text{Distance} = 5 \]

So, the distance between the points (0, 0) and (3, 4) is 5 units. This method works for any pair of points on a coordinate plane and is a fundamental concept in geometry. By understanding and applying the distance formula, you can easily determine the straight-line distance between any two points, which is a crucial skill in many areas of mathematics and science.