To find the distance between the two points \((4, 7)\) and \((7, 3)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (4, 7)\) and \((x_2, y_2) = (7, 3)\).
Substituting the coordinates into the formula:
\[ d = \sqrt{(7 - 4)^2 + (3 - 7)^2} \] \[ = \sqrt{(3)^2 + (-4)^2} \] \[ = \sqrt{9 + 16} \] \[ = \sqrt{25} \] \[ = 5 \]
So, the length between the two points is \(5\).
To determine if this length represents the side of a square, we can calculate the area of the square using the formula:
\[ \text{Area} = \text{side length}^2 \]
If we take the length of \(5\) as the side length:
\[ \text{Area} = 5^2 = 25 \]
Thus, if related to a square, the area would be \(25\).