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# Doubt in coordinate geometry-slope

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Manager
Joined: 17 Jul 2017
Posts: 244
Doubt in coordinate geometry-slope  [#permalink]

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05 Aug 2019, 19:26
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive
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do.jpg [ 3.54 MiB | Viewed 541 times ]

DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1868
Location: India
Re: Doubt in coordinate geometry-slope  [#permalink]

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05 Aug 2019, 20:20
1
For line AB, you have to consider 135 degree angle to calculate the slope
Slope of line AB= tan(135°)=-1

Slope of CD= tan120°= $$-\sqrt{3}$$

vanam52923 wrote:
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive
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Joined: 16 Oct 2010
Posts: 10490
Location: Pune, India
Re: Doubt in coordinate geometry-slope  [#permalink]

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05 Aug 2019, 22:22
vanam52923 wrote:
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive

You have to consider the angle made on the positive side of x axis.
Slope is the change in y for every unit increase in x i.e. you go from left to right. If you increase x by 1, what happens to y?
Does it increase by 1? Then slope is 1.
Does it increase by 2? Then slope is 2.
Does it decrease by 1? Then slope is -1
and so on...

Both lines you have drawn have negative slopes because going from left to right, y is decreasing.
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Karishma
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Posts: 244
Re: Doubt in coordinate geometry-slope  [#permalink]

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05 Aug 2019, 22:59
vanam52923 wrote:
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive

You have to consider the angle made on the positive side of x axis.
Slope is the change in y for every unit increase in x i.e. you go from left to right. If you increase x by 1, what happens to y?
Does it increase by 1? Then slope is 1.
Does it increase by 2? Then slope is 2.
Does it decrease by 1? Then slope is -1
and so on...

Both lines you have drawn have negative slopes because going from left to right, y is decreasing.

thank you for your response.
yes i understand that
But of these two lines which one has a greater slope, how can i answer that without finding tan /sin etc
here AB has greater angle(120) compared to CD(Cd) if i go from left to right , and one which has greate angle has greater slope so in that case Slope of AB >Cd but since bth are negative slopes so absolute value of slope of AB will be more negative compared to CD so in short CD will have greater slope compared to Ab but right answer is AB has greater slope,Can u plz explain.
Also i am ataching pic for postive slope,looking at the pic i can say slope AB >KL as Ab makes greater angle with x axis than KL
Attachments

doubt latest.jpg [ 2.09 MiB | Viewed 452 times ]

DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1868
Location: India
Doubt in coordinate geometry-slope  [#permalink]

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06 Aug 2019, 11:28
1
tan(x) is an increasing function, where x ∈ (0, 90°).
Hence if $$x_1>y_1$$, then slope of AB> slope of KL (where x_1 and y_1 lies between 0 and 90°)

tan(x) is an decreasing function, where x ∈ (90°, 180°).
Hence if $$x_1>y_1$$, then slope of AB< slope of KL (where x_1 and y_1 lies between 90° and 180°)

You don't have to find the tan values of the angles to compare the slope.

Another way to compare the slopes is to compare the increment in the y-co-ordinates of both lines, for the equal increment in the x-co-ordinates.

vanam52923 wrote:
vanam52923 wrote:
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive

You have to consider the angle made on the positive side of x axis.
Slope is the change in y for every unit increase in x i.e. you go from left to right. If you increase x by 1, what happens to y?
Does it increase by 1? Then slope is 1.
Does it increase by 2? Then slope is 2.
Does it decrease by 1? Then slope is -1
and so on...

Both lines you have drawn have negative slopes because going from left to right, y is decreasing.

thank you for your response.
yes i understand that
But of these two lines which one has a greater slope, how can i answer that without finding tan /sin etc
here AB has greater angle(120) compared to CD(Cd) if i go from left to right , and one which has greate angle has greater slope so in that case Slope of AB >Cd but since bth are negative slopes so absolute value of slope of AB will be more negative compared to CD so in short CD will have greater slope compared to Ab but right answer is AB has greater slope,Can u plz explain.
Also i am ataching pic for postive slope,looking at the pic i can say slope AB >KL as Ab makes greater angle with x axis than KL
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Posts: 10490
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Re: Doubt in coordinate geometry-slope  [#permalink]

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06 Aug 2019, 23:17
1
vanam52923 wrote:
vanam52923 wrote:
Bunuel chetan2u
Hi, please see the attached image

Which angle do we take while considering the slope?
in line AB and CD(both -ve slopes)

AB makes an angle of 45 and CD angle of 60 with x axis so slope of CD<AB as CD is more negative
but if i see external angles of same lines then AB<CD in slope as 135<120 so 135 will be more negative
So which angle do i need to consider ,please clarify

Also same doubt if slope postive

You have to consider the angle made on the positive side of x axis.
Slope is the change in y for every unit increase in x i.e. you go from left to right. If you increase x by 1, what happens to y?
Does it increase by 1? Then slope is 1.
Does it increase by 2? Then slope is 2.
Does it decrease by 1? Then slope is -1
and so on...

Both lines you have drawn have negative slopes because going from left to right, y is decreasing.

thank you for your response.
yes i understand that
But of these two lines which one has a greater slope, how can i answer that without finding tan /sin etc
here AB has greater angle(120) compared to CD(Cd) if i go from left to right , and one which has greate angle has greater slope so in that case Slope of AB >Cd but since bth are negative slopes so absolute value of slope of AB will be more negative compared to CD so in short CD will have greater slope compared to Ab but right answer is AB has greater slope,Can u plz explain.
Also i am ataching pic for postive slope,looking at the pic i can say slope AB >KL as Ab makes greater angle with x axis than KL

This is the diagram I like to keep in mind for reference. See if it helps. I never worry about angles and tan.
Attachment:

IMG_0681.JPG [ 2.33 MiB | Viewed 353 times ]

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Karishma
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Manager
Joined: 20 Jul 2012
Posts: 112
GMAT 1: 650 Q47 V33
Re: Doubt in coordinate geometry-slope  [#permalink]

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07 Aug 2019, 22:04
You always take angle from the positive x axis. So it will be counterclock wise. So the positive x axis will be at zero degree. Positive y will be at 90 degree. Negative x axis will be at 180 degree. Negative y axis will be at 270 degree

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Location: United States
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Doubt in coordinate geometry-slope  [#permalink]

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10 Aug 2019, 05:11
Hi fellow questioner,

We won't use trigonometry in the GMAT. The first thing you would want to catch when determining slope is the sign of the slope, whether it is sloping up (positive) or downwards (negative). Next, we need to figure out the magnitude. Take the 45-degree lines as a reference. Any line that is leaning closer to the y-axis than x-axis has a slope of magnitude >1. Otherwise, the slope is <1 (fractional) in magnitude. Most of the time that's all you need to know for identifying slopes. Also, keep in mind some graphs are not drawn to scale!
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Doubt in coordinate geometry-slope   [#permalink] 10 Aug 2019, 05:11

# Doubt in coordinate geometry-slope

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