To find the length of the diagonal of the square formed by the points given, we can first determine the length of the sides of the square. The points provided are:
- (1, 4)
- (3, 4)
- (1, 2)
- (3, 2)
From these points, we can see that the square has its corners at (1, 4), (3, 4), (1, 2), and (3, 2).
To find the side length of the square, we can calculate the distance between two adjacent points. For instance, we can find the distance between (1, 4) and (3, 4):
\[ \text{Distance} = |x_2 - x_1| = |3 - 1| = 2 \]
Now, since the square has equal sides, we have:
\[ \text{Side length (s)} = 2 \]
Now, to find the length of the diagonal \(d\) of the square, we can use the Pythagorean Theorem:
\[ d = \sqrt{s^2 + s^2} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]
Calculating \(2\sqrt{2}\):
\[ 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \]
Rounding to the nearest hundredth:
\[ d \approx 2.83 \]
Thus, the length of the diagonal of the square is approximately 2.83.