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A parallelogram has its four sides lying along the lines 2x + 3y = 0, 2x + 3y - 5 = 0, 3x - 4y = 0, and 3x - 4y = 3. Find the equation of the diagonal of this parallelogram that does not pass through the origin.
- 21x - 11y + 15 = 0
- 9x - 11y + 15 = 0
- 21x - 29y - 15 = 0
- 21x - 11y - 15 = 0
Correct answer: 21x - 11y - 15 = 0
Solution
The four vertices are (0,0), (9/17, -6/17), (20/17, 15/17), and (29/17, 9/17); the diagonal not through the origin connects (9/17, -6/17) and (20/17, 15/17), and its equation simplifies to 21x - 11y - 15 = 0.
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