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Three sides of a triangle are the x-axis, the y-axis and the

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Three sides of a triangle are the x-axis, the y-axis and the

by Max@Math Revolution » Thu Jan 02, 2020 11:26 pm
[GMAT math practice question]

Three sides of a triangle are the x-axis, the y-axis and the line passing through the three points (0, 2), (a, 0), (b, 4). The area of this triangle is 6. If a is negative, what is a-b?

A. 12
B. 10
C. 8
D. -10
E. -12
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by Max@Math Revolution » Sat Jan 04, 2020 11:40 pm
=>

Since the line passes through the points (0, 2), (a, 0) and (b, 4), we have (0 - 2) / (a - 0) = (4 - 2) / (b - 0), -2/a = 2/b, 2a = -2b, or a = -b.
The area of the triangle is (1/2)(-a)*2 = 6, or -a = 6. Then we have a = -6 and b = 6.
Thus we have a - b = -6 - 6 = -12.

Therefore, E is the answer.
Answer: E
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