square A′B′C′D′ has vertices A′(−2,−4), B′(−2,−11), C′(−7,−11), and D′(−7,−4)
To find the area of square A'B'C'D', we can use the distance formula to find the length of one of the sides of the square and then square that length to find the area.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
√((x2 - x1)^2 + (y2 - y1)^2)
Let's find the length of side A'B':
√((-2 - (-2))^2 + (-11 - (-4))^2)
= √(0^2 + (-7)^2)
= √49
= 7
Since A'B'C'D' is a square, all sides are the same length. Therefore, the area of the square is:
Area = side length^2
Area = 7^2
Area = 49
So, the area of square A'B'C'D' is 49 square units.