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03 Jan 2020, 00:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
68% (02:54) correct
32%
(03:36)
wrong
based on 60
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[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. \(-12\)
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. \(-12\)
Updated on: 05 Jan 2020, 00:46
Originally posted by CareerGeek on 04 Jan 2020, 21:15.
Last edited by CareerGeek on 05 Jan 2020, 00:46, edited 1 time in total.
Last edited by CareerGeek on 05 Jan 2020, 00:46, edited 1 time in total.
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MathRevolution
**Edited
Since, x and y axes are 2 sides of a triangle, the given triangle is right angled.
—> The 3 points lie in a line
—> Slopes between any 2 points are
Same
—> (0-2)/(a-0) = (4-2)/(b-0)
—> -2/a = 2/b
—> b = -a
Area of triangle = 6
—> 1/2*a*2 = 6
—> a = 6
Since “a” is negative. a = -6
—> b = -a = 6
So, a - b = -6 - 6 = -12
IMO E
Posted from my mobile device
05 Jan 2020, 00:41
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=>
Since the line passes through the points \((0, 2), (a, 0)\) and \((b, 4)\), we have \(\frac{(0 - 2) }{ (a - 0)} = \frac{(4 - 2) }{ (b - 0)}, \frac{-2}{a} = \frac{2}{b}, 2a = -2b,\) or \(a = -b.\)
The area of the triangle is \((\frac{1}{2})(-a)*2 = 6\), 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
Since the line passes through the points \((0, 2), (a, 0)\) and \((b, 4)\), we have \(\frac{(0 - 2) }{ (a - 0)} = \frac{(4 - 2) }{ (b - 0)}, \frac{-2}{a} = \frac{2}{b}, 2a = -2b,\) or \(a = -b.\)
The area of the triangle is \((\frac{1}{2})(-a)*2 = 6\), 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
