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Manager  S
Joined: 17 Jul 2017
Posts: 117
Doubt in coordinate geometry-slope  [#permalink]

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Bunuel chetan2u
VeritasKarishma
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
Attachments do.jpg [ 3.54 MiB | Viewed 362 times ]

Director  P
Joined: 19 Oct 2018
Posts: 776
Location: India
Re: Doubt in coordinate geometry-slope  [#permalink]

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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
VeritasKarishma
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
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9551
Location: Pune, India
Re: Doubt in coordinate geometry-slope  [#permalink]

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vanam52923 wrote:
Bunuel chetan2u
VeritasKarishma
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.
_________________
Karishma
Veritas Prep GMAT Instructor

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Manager  S
Joined: 17 Jul 2017
Posts: 117
Re: Doubt in coordinate geometry-slope  [#permalink]

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VeritasKarishma wrote:
vanam52923 wrote:
Bunuel chetan2u
VeritasKarishma
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 273 times ]

Director  P
Joined: 19 Oct 2018
Posts: 776
Location: India
Doubt in coordinate geometry-slope  [#permalink]

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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:
VeritasKarishma wrote:
vanam52923 wrote:
Bunuel chetan2u
VeritasKarishma
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
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9551
Location: Pune, India
Re: Doubt in coordinate geometry-slope  [#permalink]

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1
vanam52923 wrote:
VeritasKarishma wrote:
vanam52923 wrote:
Bunuel chetan2u
VeritasKarishma
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 174 times ]

_________________
Karishma
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Manager  B
Joined: 20 Jul 2012
Posts: 99
GMAT 1: 650 Q47 V33 Re: Doubt in coordinate geometry-slope  [#permalink]

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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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Manager  B
Joined: 17 Sep 2014
Posts: 87
Location: United States
GMAT 1: 780 Q51 V45 GRE 1: Q170 V167 Doubt in coordinate geometry-slope  [#permalink]

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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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