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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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New post 29 Oct 2014, 08:11
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A
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D
E

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  25% (medium)

Question Stats:

71% (01:29) correct 29% (01:31) wrong based on 390 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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New post 30 Oct 2014, 07:16
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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

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

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New post 25 Sep 2017, 14:41
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

Answer is E


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

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New post 09 Dec 2017, 20:01
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
in answer options and check.
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Which of the following equations represents a line that is perpendicul  [#permalink]

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New post 09 Dec 2017, 21:09
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adkikani wrote:
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
in answer options and check.


Hi adkikani

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.
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Which of the following equations represents a line that is perpendicul &nbs [#permalink] 09 Dec 2017, 21:09
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