Determine the distance between \( A(0,0) \) and \( B(4,3) \)

To determine the distance between points \( A(0, 0) \) and \( B(4, 3) \), you can use the **distance formula**, which is derived from the Pythagorean theorem. The distance formula is given by: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] **Step-by-Step Calculation:** 1. **Identify the coordinates:** - Point \( A \) has coordinates \( (x_1, y_1) = (0, 0) \). - Point \( B \) has coordinates \( (x_2, y_2) = (4, 3) \). 2. **Substitute the values into the distance formula:** \[ \text{Distance} = \sqrt{(4 - 0)^2 + (3 - 0)^2} \] 3. **Calculate the differences:** \[ \text{Distance} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} \] 4. **Add the squared differences:** \[ \text{Distance} = \sqrt{25} \] 5. **Take the square root:** \[ \text{Distance} = 5 \] **Conclusion:** The distance between points \( A(0, 0) \) and \( B(4, 3) \) is **5 units**.