Show that the points `(1,\ 7),\ (4,\ 2),\ (-1,\ -1)\ a n d\ (\- 4,\ 4)` are the vertices of a square.

Explanation

To show that the points \( (1, 7), (4, 2), (-1, -1), \) and \( (-4, 4) \) are the vertices of a square, we will follow these steps:

### Step 1: Calculate the lengths of the sides
We will use the distance formula to find the lengths of the sides \( AB, BC, CD, \) and \( DA \).

The distance formula is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
...