Square ABCD has vertices A(-2, -3), B(4, -1), C(2, 5), and D(-4, 3). What is the area of the square?Question 8Select one:a.40 units2b.25.28 units2c.28.25 units2d.400 units2

To find the area of the square, we first need to find the length of one of its sides. We can use the distance formula to find the length of side AB:

The distance formula is √[(x₂ - x₁)² + (y₂ - y₁)²]

For points A(-2, -3) and B(4, -1), the distance (AB) is:

AB = √[(4 - (-2))² + ((-1) - (-3))²] AB = √[(6)² + (2)²] AB = √[36 + 4] AB = √40

Since ABCD is a square, all sides are equal, so the length of each side is √40 units.

The area of a square is given by the formula side². So, the area of square ABCD is:

Area = (√40)² Area = 40 units²

So, the correct answer is a. 40 units².

To find the area of the square, we first need to find the length of one of its sides. We can use the distance formula to find the length of side AB:

The distance formula is √[(x₂ - x₁)² + (y₂ - y₁)²]

For points A(-2, -3) and B(4, -1), the distance (AB) is:

AB = √[(4 - (-2))² + ((-1) - (-3))²] AB = √[(6)² + (2)²] AB = √[36 + 4] AB = √40

Since ABCD is a square, all sides are equal, so the length of each side is √40 units.

The area of a square is given by the formula side². So, the area of square ABCD is:

Area = (√40)² Area = 40 units²

So, the correct answer is a. 40 units².