Straight Lines
Area of Parallelogram
Premium Question
Grade 11
Question:
The area of the parallelogram formed by the four lines $y = mx, y = mx + 1, y = nx$ and $y = nx + 1$ ($m \neq n$) is:
(1) $\frac{|m + n|}{|m - n|}$
(2) $\frac{2}{|m - n|}$
(3) $\frac{1}{|m - n|}$
(4) $\frac{1}{|m + n|}$
Step-by-Step Solution
Key Concept: The distance between the parallel pair $y = mx$ and $y = mx + 1$ is $1/\sqrt{1 + m^2}$. Similarly for the other pair. Divide product by $\sin(\text{included angle})$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)