Final answer:
The perimeter of the quadrilateral formed by the points A, B, C, and D is calculated by finding the distances between each pair of points and adding them together. The perimeter is approximately 25.37 units.
Step-by-step explanation:
A mathematically correct question using all four points A (-1, 2), B (5, 2), C (1, 3), and D (-1, -5) could be: Determine the perimeter of the quadrilateral formed by the points A, B, C, and D.
To solve this, we'll first find the lengths of the sides of the quadrilateral by calculating the distance between each pair of points.
Firstly, calculate the distance between A and B (both have the same y-coordinate, so we can just subtract their x-coordinates):
AB = |xB - xA| = |5 - (-1)| = 6 units.
Secondly, calculate the distance between B and C using the distance formula:
d = √((x2 - x1)2 + (y2 - y1)2)
BC = √((1 - 5)2 + (3 - 2)2) = √(16 + 1) = √17 ≈ 4.12 units.
Next, calculate the distance between C and D:
CD = √((-1 - 1)2 + (-5 - 3)2) = √(4 + 64) = √68 ≈ 8.25 units.
Finally, calculate the distance between D and A (they have the same x-coordinate):
DA = |yD - yA| = | -5 - 2| = 7 units.
Now add the lengths of all sides to get the perimeter:
Perimeter = AB + BC + CD + DA = 6 + 4.12 + 8.25 + 7 = 25.37 units.