What is the area (in square units) of the rectangle enclosed by the lines x = −4, x = 2, y = −2 and y = 3 in the Cartesian plane?

Introduction / Context:
This question tests the ability to interpret straight line equations in the coordinate plane and compute the area of the rectangular region they enclose. It is a straightforward application of distance between parallel lines and the area formula for a rectangle.

Given Data / Assumptions:

• Vertical boundary lines: x = −4 and x = 2.
• Horizontal boundary lines: y = −2 and y = 3.
• The region enclosed by these four lines is a rectangle.
• We must find its area in square units.

Concept / Approach:
A rectangle formed by two vertical and two horizontal lines has side lengths equal to the differences in the corresponding coordinates:

• Width (horizontal side) = difference in x values = x_right − x_left.
• Height (vertical side) = difference in y values = y_top − y_bottom.

Step-by-Step Solution:
Step 1: Identify the left and right boundaries: x = −4 and x = 2. Step 2: Compute width = x_right − x_left = 2 − (−4) = 2 + 4 = 6 units. Step 3: Identify the bottom and top boundaries: y = −2 and y = 3. Step 4: Compute height = y_top − y_bottom = 3 − (−2) = 3 + 2 = 5 units. Step 5: Compute area = width * height = 6 * 5 = 30 square units.

Verification / Alternative check:
Plotting the points of intersection of the lines confirms a rectangle with vertices at (−4, −2), (2, −2), (2, 3) and (−4, 3). The horizontal distance from (−4, −2) to (2, −2) is 6 units, and the vertical distance from (2, −2) to (2, 3) is 5 units. Multiplying these side lengths again yields 30 square units, reinforcing the calculation.

Why Other Options Are Wrong:
12 and 24: These correspond to smaller areas and would result from using only one dimension correctly or using incorrect differences between coordinates.
60: This is double the correct area and could arise if one mistakenly took both directions as 10 units (for example by misreading the lines) and then multiplied.
15: This might appear if someone added lengths and then halved incorrectly, but it does not correspond to the true area of the rectangle.

Common Pitfalls:
Students sometimes forget to subtract negative values correctly, leading to incorrect side lengths. Remember that subtracting a negative is equivalent to adding the absolute value. Another mistake is to confuse the coordinate values with distances directly without considering their difference.

Final Answer:
The area of the rectangle is 30 square units.