Question

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

Answer 1

To find the area of the rectangle ABCD, we can use the formula for finding the area of a rectangle which is length x width.

To find the length of the rectangle AB, we use the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Length AB = √((5 - 2)^2 + (-5 - (-5))^2)
Length AB = √(3^2 + 0^2) = √(9) = 3 miles

To find the width of the rectangle AB, we use the same distance formula between points C and D:

Width CD = √((5 - 2)^2 + (-1 - (-5))^2)
Width CD = √(3^2 + 4^2) = √(9 + 16) = √(25) = 5 miles

Now, we can find the area of the rectangle ABCD:

Area = length x width
Area = 3 miles x 5 miles
Area = 15 square miles

So, the area of the rectangle ABCD is 15 square miles.