To find the distance between the points \((6,7)\) and \((7,4)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Let \((x_1, y_1) = (6, 7)\) and \((x_2, y_2) = (7, 4)\).
Now substitute the values into the formula:
\[ d = \sqrt{(7 - 6)^2 + (4 - 7)^2} \]
Calculating the differences:
\[ d = \sqrt{(1)^2 + (-3)^2} \]
Now simplify further:
\[ d = \sqrt{1 + 9} = \sqrt{10} \]
Thus, the distance between the points \((6, 7)\) and \((7, 4)\) is
\[ \sqrt{10} \text{ units}. \]