Find the area of rectangle ABCD , with vertices A(1,7) , B(3,7) , C(3,−4) , and D(1,−4) .(1 point)
To find the area of the rectangle ABCD, we can use the formula:
Area = length * width
To find the length and width of the rectangle, we can use the distance formula between two points:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula:
1. Length = distance between points A and B
Length = √((3-1)^2 + (7-7)^2)
Length = √2^2 + 0
Length = √4
Length = 2
2. Width = distance between points B and C
Width = √((3-3)^2 + (7-(-4))^2)
Width = √0^2 + 11^2
Width = √121
Width = 11
Now we can calculate the area of the rectangle:
Area = length * width
Area = 2 * 11
Area = 22
Therefore, the area of rectangle ABCD is 22 square units.