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Math Revolution GMAT Instructor V
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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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. $$-12$$

_________________
VP  V
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]

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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 V
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]

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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 $$a – b = -6 – 6 = -12.$$

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Manager  B
Joined: 21 Feb 2017
Posts: 140
Re: Three sides of a triangle are the x-axis, the y-axis and the line pass  [#permalink]

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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  V
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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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, 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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