Answer :
Final answer:
The area of rectangle with vertices P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3) is calculated by finding the lengths of the sides (PQ and QR) using the distance formula and then computing the area using the formula Area = length x width. The result is approximately 60 square units. Thus the correct option is a. 60 square units.
Explanation:
In order to find the area of a rectangle given its vertices, we first need to calculate the lengths of the sides. The vertices given are P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3). We'll assume that P and Q form one side, and Q and R form another side.
The formula for calculating the distance between two points in a 2D space is d = √((x₂ - x₁)² + (y₂ - y₁)²). Using this formula, we find that PQ = √((4-2)² + (-1-3)²) = √(4+16) = √(20) = 4.47 units (approx). Similarly, QR =√((-8-4)² + (-7-(-1))²) = √(144+36) =√(180) = 13.42 units (approx).
Now that we know the lengths of two sides of the rectangle, we can calculate the area using the formula Area = length x width. That gives us 4.47 units × 13.42 units = 59.99 square units, which is approximately 60 square units.
Hence, "a. 60 square units" is the correct option.
Learn more about Area of Rectangle here: brainly.com/question/14937626
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