Question

a = (3, 2), b = (7.5, 2), c = (7.5, -2.5), d = (3, -2)

Explanation:

Assuming the problem is to find the area of the rectangle formed by points \( A(3, 2) \), \( B(7.5, 2) \), \( C(7.5, -2) \), \( D(3, -2) \) (correcting \( C \) to \( (7.5, -2) \) for a rectangle, as the given \( C(7.5, -2.5) \) might be a typo).

Step 1: Find the length of \( AB \)

The distance between \( A(3, 2) \) and \( B(7.5, 2) \) is calculated using the formula for the distance between two points with the same \( y \)-coordinate: \( \text{Length} = |x_2 - x_1| \).
\( AB = |7.5 - 3| = 4.5 \)

Step 2: Find the length of \( AD \)

The distance between \( A(3, 2) \) and \( D(3, -2) \) is calculated using the formula for the distance between two points with the same \( x \)-coordinate: \( \text{Length} = |y_2 - y_1| \).
\( AD = |-2 - 2| = 4 \)

Step 3: Calculate the area of the rectangle

The area of a rectangle is \( \text{Area} = \text{length} \times \text{width} \). Here, \( \text{length} = AB = 4.5 \) and \( \text{width} = AD = 4 \).
\( \text{Area} = 4.5 \times 4 = 18 \)

Answer:

The area of the rectangle (assuming \( C \) is \( (7.5, -2) \)) is \( 18 \).

If the problem was different (e.g., identifying the shape, checking coordinates), adjust the steps accordingly. Since the original problem wasn't specified, this is a common problem with these coordinates.