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What is the equation of a line perpendicular to lines [#permalink]
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11 Nov 2012, 15:52
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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12 Nov 2012, 00:14
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:
(y2y1)/(x2x1)
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.
So for your equation: y=2x+5
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, 02:40
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:
(y2y1)/(x2x1)
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.
So for your equation: y=2x+5
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, 04:35
No, you can't have two equations for the same line (unless you multiply by different nonzero 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, 15:39
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, 20:18
Firstly, there can be an infinite number of perpendicular lines to the two equations you posted. You will need some other condition to pinpoint 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, 22:56
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 pinpoint 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=2x5) 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, 04:26
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 pinpoint 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=2x5) 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: mathcoordinategeometry87652.html
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