What is the equation of a line perpendicular to lines : GMAT Quantitative Section
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# What is the equation of a line perpendicular to lines

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What is the equation of a line perpendicular to lines [#permalink]

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11 Nov 2012, 14:52
What is the equation of a line perpendicular to lines
Y = 2x + 5
and Y = 2X - 10

I just want get my concept cleared, this question is framed by myself from an explanation of a question.
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Re: What is the equation of a line perpendicular to lines [#permalink]

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11 Nov 2012, 23:14
It is not very difficult. Just note that slope of the line is how inclined it is with respect to the x axis.

For instance, if we have 2 coordinates: (x1,y1) and (x2,y2), we can calculate the slope(gradient) as follows:

(y2-y1)/(x2-x1)

Slope of a line is denoted by m. You can look at the line equation:

y= mx+c.

Here m is the slope and c is the y intercept or where the line cuts the y axis. In your example, just substitute x=0 in the equation and solve for y.

I do not want to go into details, but the product of the slopes of two perpendicular lines must equal -1.

slope of this line is 2. Therefore any perpendicular line will have the slope as -1/2 since the product of 2 and -1/2 is -1.

Therefore the perpendicular will take the form: y= (-1/2)x +k, where k is the y intercept of the perpendicular line...
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Re: What is the equation of a line perpendicular to lines [#permalink]

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12 Nov 2012, 01:40
seriousmonkey wrote:
It is not very difficult. Just note that slope of the line is how inclined it is with respect to the x axis.

For instance, if we have 2 coordinates: (x1,y1) and (x2,y2), we can calculate the slope(gradient) as follows:

(y2-y1)/(x2-x1)

Slope of a line is denoted by m. You can look at the line equation:

y= mx+c.

Here m is the slope and c is the y intercept or where the line cuts the y axis. In your example, just substitute x=0 in the equation and solve for y.

I do not want to go into details, but the product of the slopes of two perpendicular lines must equal -1.

slope of this line is 2. Therefore any perpendicular line will have the slope as -1/2 since the product of 2 and -1/2 is -1.

Therefore the perpendicular will take the form: y= (-1/2)x +k, where k is the y intercept of the perpendicular line...

My doubt is really a basic one

I also solved till slope but know the y intercept can have two different values as you see we have two different equations... so we can have two different equations for the same line.... Is it possible?
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Re: What is the equation of a line perpendicular to lines [#permalink]

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12 Nov 2012, 03:35
No, you can't have two equations for the same line (unless you multiply by different non-zero constants on both sides- but it boils down to the same thing really)

the two equations you gave are parallel lines: they have the same slope but they cut the y axis and x axis at different points.
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Re: What is the equation of a line perpendicular to lines [#permalink]

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12 Nov 2012, 14:39
Archit143 wrote:
What is the equation of a line perpendicular to lines
Y = 2x + 5
and Y = 2X - 10

I just want get my concept cleared, this question is framed by myself from an explanation of a question.

Kkk

the slope for the perpendicular line will be -1/2
and y intercept from Y = 2x + 5 will be 5 hence equation that follows from it is Y = -1/2X + 5

and Y intercept from y = 2x - 10 will be -10 hence the equation that follows from it Y = -1/2 X - 10

The two eqns are of the perpendicular lines

hence which one to take as final answer or both can b correct answer.
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Re: What is the equation of a line perpendicular to lines [#permalink]

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12 Nov 2012, 19:18
Firstly, there can be an infinite number of perpendicular lines to the two equations you posted. You will need some other condition to pin-point the line you need to get the answer( such as "the perpendicular line passes through a point" or something). So that is why I posted y= -1/2*x +k, because we can have any value of k and it will be perpendicular to the straight lines you posted (try plotting the lines and draw perpendicular lines- you will find you can draw many)
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Re: What is the equation of a line perpendicular to lines [#permalink]

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21 Nov 2012, 21:56
seriousmonkey wrote:
Firstly, there can be an infinite number of perpendicular lines to the two equations you posted. You will need some other condition to pin-point the line you need to get the answer( such as "the perpendicular line passes through a point" or something). So that is why I posted y= -1/2*x +k, because we can have any value of k and it will be perpendicular to the straight lines you posted (try plotting the lines and draw perpendicular lines- you will find you can draw many)

Hey thanks dude..
I was looking for similar thing..

I have another doubt...
ways to find a equation of perpendicular line y=mx+k...
such as:
1) one point and one equation of line (y=2x-5) or
2) one point and one slope of another line (m=2)

Is there any way to find this equation of perpendicular line?
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Re: What is the equation of a line perpendicular to lines [#permalink]

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22 Nov 2012, 03:26
shanmugamgsn wrote:
seriousmonkey wrote:
Firstly, there can be an infinite number of perpendicular lines to the two equations you posted. You will need some other condition to pin-point the line you need to get the answer( such as "the perpendicular line passes through a point" or something). So that is why I posted y= -1/2*x +k, because we can have any value of k and it will be perpendicular to the straight lines you posted (try plotting the lines and draw perpendicular lines- you will find you can draw many)

Hey thanks dude..
I was looking for similar thing..

I have another doubt...
ways to find a equation of perpendicular line y=mx+k...
such as:
1) one point and one equation of line (y=2x-5) or
2) one point and one slope of another line (m=2)

Is there any way to find this equation of perpendicular line?

Check here: math-coordinate-geometry-87652.html
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Re: What is the equation of a line perpendicular to lines   [#permalink] 22 Nov 2012, 03:26
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