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

Question

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

Bunuel · Accepted Answer

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.

jakelong1 · Answer

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

ronr34 · Answer

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?

earnit · Answer

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?

Bunuel · Answer

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.

earnit · Answer

Bunuel: Hope it's Clear Me: Crystal.

Thank you.

Nunuboy1994 · Answer

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.

Mayur21 · Answer

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

kinshuk97gupta · Answer

I have one doubt regarding this question. I get it that you chose 90 degrees because of the slopes. But it also says that these lines don't intersect which means they are parallel. So the angle should be 0 degrees isn't it?

Posted from my mobile device

Abhibarua · Answer

An excellent question that tests multiple co-ordinate geometry concepts without requiring tons of calculation.

Slope of line l is 5 (y = 5x + 4)

Since line k does not intersect line l, line k & l are parallel.

So, slope of line k is also 5.

Slope of line w is -1/5 (Derived from 10y + 2x + 20 = 0)

So, line k & w are perpendiculars to each other. In other words, the angle formed by line k and line w is 90 degree.

Option: D

HansJK · Answer

"Since the slopes of the lines are negative reciprocals of each other then these lines are perpendicular to each other (Bunuel)."

Can someone explain or show why this is? Do you have to memorize this fact to get the question right, or is there another way?

Thank you!!

Abhibarua · Answer

Yes, GMAT expects you to know this.

You can draw a line with a slope of 5 and another line with a slope of -1/5. The lines will be perpendiculars to each other.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards