To find the distance between the points \((4, 3)\) and \((2, -1)\), we use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Where:
- \((x_1, y_1) = (4, 3)\)
- \((x_2, y_2) = (2, -1)\)
Now we can plug in the values:
\[ d = \sqrt{(2 - 4)^2 + (-1 - 3)^2} \]
Calculating the differences:
\[ d = \sqrt{(-2)^2 + (-4)^2} \]
Calculating the squares:
\[ d = \sqrt{4 + 16} \]
Adding the results:
\[ d = \sqrt{20} \]
We can simplify \(\sqrt{20}\):
\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \]
Thus, the distance between the points \((4, 3)\) and \((2, -1)\) is
\[ \boxed{2\sqrt{5}} \]