Geometry

Question Analysis:
This question tests the ability to calculate side lengths of a quadrilateral using the distance formula and then sum them to find the perimeter.
The main focus is on applying the distance formula correctly to all four sides.

Key Concept Explanation:
The distance formula is essential for determining the length of a line segment between two points in the coordinate plane.
The perimeter of a polygon is the sum of the lengths of all its sides.

Step-by-Step Solution:
First, calculate each side length using the distance formula:
For AB: √[(4-1)² + (5-2)²] = √(9 + 9) = √18 = 3√2
For BC: √[(7-4)² + (2-5)²] = √(9 + 9) = 3√2
For CD: √[(4-7)² + (-1-2)²] = 3√2
For DA: √[(1-4)² + (2-(-1))²] = 3√2
Then sum all sides...