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# Which of the following equations represents a line that is perpendicul

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Which of the following equations represents a line that is perpendicul  [#permalink]

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29 Oct 2014, 09:11
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Difficulty:

25% (medium)

Question Stats:

68% (00:53) correct 32% (00:48) wrong based on 380 sessions

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Tough and Tricky questions: Coordinate Geometry.

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8?

A. 3x + 4y = 18
B. 3x – 4y = 24
C. 4y – 3x = 26
D. 1.5y + 2x = 18
E. 8x – 6y = 24

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Re: Which of the following equations represents a line that is perpendicul  [#permalink]

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30 Oct 2014, 08:16
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1
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8?

A. 3x + 4y = 18
B. 3x – 4y = 24
C. 4y – 3x = 26
D. 1.5y + 2x = 18
E. 8x – 6y = 24

Writing 3x + 4y = 8 in the slope intercept form Y = mx + c; we get

y = 2 - (3/4) x

slope of line = - 3/4

Slope of line perpendicular to above line = 4/3

Testing options that give a slope of 4/3

a) 3x + 4y =18
Slope = -3/4

b) 3x - 4y = 24
Slope = 3/4

c) 4y - 3x = 26
Slope = 3/4

d) 1.5y + 2x = 18
Slope = -2/1.5

e) 8x - 6y = 24
Slope = 4/3

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Re: Which of the following equations represents a line that is perpendicul  [#permalink]

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25 Sep 2017, 15:41
1
Ashishmathew01081987 wrote:
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8?

A. 3x + 4y = 18
B. 3x – 4y = 24
C. 4y – 3x = 26
D. 1.5y + 2x = 18
E. 8x – 6y = 24

Writing 3x + 4y = 8 in the slope intercept form Y = mx + c; we get

y = 2 - (3/4) x

slope of line = - 3/4

Slope of line perpendicular to above line = 4/3

Testing options that give a slope of 4/3

a) 3x + 4y =18
Slope = -3/4

b) 3x - 4y = 24
Slope = 3/4

c) 4y - 3x = 26
Slope = 3/4

d) 1.5y + 2x = 18
Slope = -2/1.5

e) 8x - 6y = 24
Slope = 4/3

Thanks. I didn't know how to get the perpendicular slope, but google led me to this great and simple khan academy video: https://youtu.be/0671cRNjeKI

Basically, the product of the slopes of two perpendicular lines must be "-1" (they are exactly the oppose). If they were parallel, the slopes' product would be "+1" (same direction).

So, the perpendicular slope must be the NEGATIVE of the RECIPROCAL of the original slope. E.g.: m = 3/4, it's reciprocal would be 1/(3/4) = 4/3. The negative of the reciprocal: - 4/3.

Hope it helps
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Re: Which of the following equations represents a line that is perpendicul  [#permalink]

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09 Dec 2017, 21:01
Bunuel VeritasPrepKarishma niks18

Although I got this correct i took more time since
I first found slope of given line in question stem and thought
to simply find line whose slope is 4/3 by substituiting slope
given line in Q stem. Since that did not work, I had to take each slope
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Which of the following equations represents a line that is perpendicul  [#permalink]

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09 Dec 2017, 22:09
1
Bunuel VeritasPrepKarishma niks18

Although I got this correct i took more time since
I first found slope of given line in question stem and thought
to simply find line whose slope is 4/3 by substituiting slope
given line in Q stem. Since that did not work, I had to take each slope

I assume you should not take more than 10 seconds to calculate the slope of the original equation $$3x + 4y = 8$$

so $$m_1=-\frac{3}{4}$$, Now as the lines are perpendicular so the slope of the other line say $$m_2$$ will be

$$m_1*m_2=-1 => m_2=\frac{4}{3}$$

equation of any straight line is $$y=mx+c$$, so the equation of perpendicular line will be

$$y=\frac{4}{3}x+c$$

$$=>3y-4x=c$$ -----------(1), where $$c$$ is any constant

Now check the options you will notice option A, B, C & D none are of the form as equation 1 and you can visually eliminate them. Only equation E can be written as

$$8x – 6y = 24 => 3y-4x=-12$$ this is same as equation (1). hence our answer

this entire process should not take more than a minute.

Other option can be to calculate slope of each option and check which will take few more seconds but I guess should be solvable within 2 minutes.
Which of the following equations represents a line that is perpendicul &nbs [#permalink] 09 Dec 2017, 22:09
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