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Line l is defined by the equation y – 5x = 4 and line w is d

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Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 24 Feb 2013, 03:56
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Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 24 Feb 2013, 05:35
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mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

Answer: D.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 24 Feb 2013, 06:03
1
Line L equation : y = 5x + 4

I think the wording of your problem got messed up... i.e. there is some typo error...

So Assuming 10y + 2x = 20 is line K. The equation of line K : = 10y = -2x - 20. Dividing by 10 throughout we get
y = ( -1/5 ) x - 2

Slope of line L = m1 = 5
Slope of line K = m2 = -1/5

The standard rule says that if the product of two slope is -1 then the two lines are perpendicular

m1 * m2 = > 5 * - 1/5 = -1

Hence the answer is D i.e. 90

Hope this helps
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 28 Sep 2014, 06:48
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

Answer: D.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.

Hi Bunuel,
If we are given two lines (and know their slopes), can we calculate the degree that their intersection makes?
What's the formula for that?
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 10 Nov 2014, 08:20
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

Answer: D.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.



Bunuel,
Sorry for my ignorance but is it a fact that two lines in any plane, if they don't intersect, they MUST be parallel?
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 10 Nov 2014, 08:29
earnit wrote:
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

Answer: D.

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

PS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=41
DS questions on Coordinate Geometry: search.php?search_id=tag&tag_id=62

Hope it helps.



Bunuel,
Sorry for my ignorance but is it a fact that two lines in any plane, if they don't intersect, they MUST be parallel?


On the GMAT, all figures lie in a plane unless otherwise indicated. So, lines l, w and k are in the same plane. Next, if two lines that are in the same plane do not intersect, the two lines are parallel. Thus, line k does not intersect line l, means that lines k and l are parallel.

Hope it's clear.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Extra-hard Quant Tests with Brilliant Analytics

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Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 10 Nov 2014, 08:32
Bunuel: Hope it's Clear

Me: Crystal. :)

Thank you.
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 14 Jun 2017, 20:40
1
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


It is important to understand and have a visual map of this question- what this questions basically means when it states that all lines lie in one plane simply means- well within the context of the GMAT as Bunuel already stated- that all lines exist on a two dimensional plane. So if you draw out a chart/ plane with 4 quadrants as usual on a piece of paper then there's no way to have two lines that do not intersect and are not parallel. In simpler terms, if two lines do not intersect then they MUST be parallel. Also, do not confuse line k with l or w- basically this question gives you two equations for two lines because these lines are perpendicular.

Line L
10y= -2x -20=
y = -2/10x - 20
y= -1/5x - 2

Line W
y= 4 +5x
y= 5x + 4 ( commutative property of addition)

Because line K does not intersect L it MUST be parallel to L and if line K is parallel to L then it is also perpendicular to W- and perpendicular simply means it forms a 90 degree angle. Perpendicular lines are also important for circle questions on the GMAT. Some of the concepts should hopefully carry over- so some of the common traps and shortcuts in coordinate geometry problems on the GMAT will help with PS and DS questions in regular geometry and vice versa.
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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New post 15 Jun 2017, 09:20
ronr34 wrote:
Bunuel wrote:
mun23 wrote:
Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w? (Assume that all lines lie in one coordinate plane.)

(A) 0
(B) 30
(C) 60
(D) 90
(E) It cannot be determined from the information given

I am really afraid of co-ordinate geometry.I always find it quite difficult.Plz need detail explanation.anyone plz help me


The equation of line l is y = 5x + 4 --> thus its slope is 5.
The equation of line w is y = -1/5*x - 2 --> thus its slope is -1/5.

Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other.

Next, lines l and k are parallel, hence line perpendicular to line l will be perpendicular to line k too. So, lines k and w are also perpendicular to each other.

Answer: D.

For more on Coordinate Geometry check: http://gmatclub.com/forum/math-coordina ... 87652.html

PS questions on Coordinate Geometry: http://gmatclub.com/forum/search.php?se ... &tag_id=41
DS questions on Coordinate Geometry: http://gmatclub.com/forum/search.php?se ... &tag_id=62

Hope it helps.

Hi Bunuel,
If we are given two lines (and know their slopes), can we calculate the degree that their intersection makes?
What's the formula for that?

Yes. Use the formula

TanX = m1-m2/(1+m1m2)

where X is the angle between the lines and m1 and m2 are the slopes.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Re: Line l is defined by the equation y – 5x = 4 and line w is d  [#permalink]

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