Find the area of rectangle ABCD That has vertices point A (2, -5), point B (5, -5), point C (5, -1), and point D ( 2, -1) in square miles.
To find the area of the rectangle, we need to calculate the distance between points A and B (which is the length of the rectangle) and between points A and D (which is the width of the rectangle).
Using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
1. Distance between points A and B:
√((5-2)^2 + (-5-(-5))^2)
= √(3^2 + 0^2)
= √(9)
= 3 miles
2. Distance between points A and D:
√((2-2)^2 + (-1-(-5))^2)
= √(0 + 16)
= √(16)
= 4 miles
The area of the rectangle is then:
Area = length x width
Area = 3 miles x 4 miles
Area = 12 square miles
Therefore, the area of rectangle ABCD is 12 square miles.