Find the area of rectangle ABCD, with vertices A(1,7), B(3,7), C(3,−4), and D(1,−4).
To find the area of a rectangle, we can use the formula:
Area = base x height
First, let's find the length of side AB. Using the distance formula:
d = √((x2-x1)^2 + (y2-y1)^2)
d = √((3-1)^2 + (7-7)^2)
d = √(2^2 + 0^2)
d = √4
d = 2
So, the length of side AB is 2.
Next, let's find the length of side AD. Using the distance formula:
d = √(1-1)^2 + (-4-7)^2)
d = √(0^2 + (-4-7)^2)
d = √(0 + (-11)^2)
d = √121
d = 11
So, the length of side AD is 11.
Since a rectangle has opposite sides that are equal in length, the base of the rectangle is AB and the height of the rectangle is AD.
Area = base x height
Area = 2 x 11
Area = 22
Therefore, the area of rectangle ABCD is 22 square units.