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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8572
GMAT 1: 760 Q51 V42
GPA: 3.82
Three sides of a triangle are the x-axis, the y-axis and the line pass  [#permalink]

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02 Jan 2020, 23:42
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Difficulty:

55% (hard)

Question Stats:

63% (02:54) correct 37% (03:34) wrong based on 27 sessions

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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. $$-12$$

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 20 Jul 2017 Posts: 1321 Location: India Concentration: Entrepreneurship, Marketing WE: Education (Education) Three sides of a triangle are the x-axis, the y-axis and the line pass [#permalink] ### Show Tags Updated on: 04 Jan 2020, 23:46 2 MathRevolution wrote: [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. $$-12$$ **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 Originally posted by Dillesh4096 on 04 Jan 2020, 20:15. Last edited by Dillesh4096 on 04 Jan 2020, 23:46, edited 1 time in total. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8572 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Three sides of a triangle are the x-axis, the y-axis and the line pass [#permalink] ### Show Tags 04 Jan 2020, 23:41 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Joined: 21 Feb 2017
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Re: Three sides of a triangle are the x-axis, the y-axis and the line pass  [#permalink]

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27 Jan 2020, 06:43
Dillesh4096 wrote:
MathRevolution wrote:
[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. $$-12$$

**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

Hi what property is this? "Since x and y axes are 2 sides of a triangle, the given triangle is right-angled."
VP
Joined: 20 Jul 2017
Posts: 1321
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: Three sides of a triangle are the x-axis, the y-axis and the line pass  [#permalink]

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27 Jan 2020, 07:57
1
Kritisood wrote:
Hi what property is this? "Since x and y axes are 2 sides of a triangle, the given triangle is right-angled."

Hi Kritisood,

Please see the attached image

As we can clearly see, the angle between x & y axis is 90 degrees.
So, the triangle OAC is right angled

Hope it's clear!
Attachments

1.png [ 6.96 KiB | Viewed 192 times ]

Re: Three sides of a triangle are the x-axis, the y-axis and the line pass   [#permalink] 27 Jan 2020, 07:57
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# Three sides of a triangle are the x-axis, the y-axis and the line pass

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