The coordinates you've provided form a rectangle:

• Point 1: (1,1)
• Point 2: (1,5)
• Point 3: (5,5)
• Point 4: (5,1)

To find the perimeter of this rectangle, we first calculate the lengths of the sides. A rectangle has two pairs of equal sides:

1. Length of the side between (1,1) and (1,5):
   This side is a vertical line, so we calculate the difference in the y-coordinates.
   $|5 - 1| = 4$

2. Length of the side between (1,1) and (5,1):
   This side is a horizontal line, so we calculate the difference in the x-coordinates.
   $|5 - 1| = 4$

Thus, both vertical sides are 4 units long and both horizontal sides are 4 units long.

Perimeter Formula for a Rectangle:

$\text{Perimeter} = 2 \times (\text{Length} + \text{Width})$ Since both sides have the same length and width (4 units), the perimeter is: $\text{Perimeter} = 2 \times (4 + 4) = 2 \times 8 = 16 \text{ units}$

Final Answer:

The perimeter of the rectangle is 16 units.

Would you like more details or have any further questions? Here are some related questions to explore:

1. How do you find the area of a rectangle given the coordinates of its corners?
2. What is the distance formula for finding the length of a side between two points in coordinate geometry?
3. How would the perimeter change if the coordinates were different (e.g., (2,2), (2,6), (6,6), (6,2))?
4. What happens to the perimeter of a rectangle if the shape becomes a square?
5. How do you calculate the perimeter of a polygon with more than four sides?

Tip: To calculate the perimeter of any polygon, simply sum up the lengths of all its sides.