Find the area of the parallelogram whose sides lie along the lines 14x - 21y + 15 = 0, 14x - 21y - 6 = 0, 2x - 6y + 9 = 0, and 2x - 6y - 3 = 0.

Correct answer: 6

Solution

Rewriting: pair 1 gives |c gap| = |(-15)-(6)| = 21 (using 14x-21y = -15 and 14x-21y = 6); pair 2 gives |c gap| = |(-9)-(3)| = 12. The cross-determinant |14*(-6)-2*(-21)| = |-84+42| = 42. Area = (21*12)/42 = 6.

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