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# In the xy plane line m has the equation 4x + y = k. Line n

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In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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06 Mar 2012, 10:37
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In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!
[Reveal] Spoiler: OA

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06 Mar 2012, 11:46
This is an interesting problem, and I haven't solved it either as I am still learning this stuff. so far I've gotten about 3 different wrong answers.

I re wrote the equation of the line M: to Y=-4x + k

Given that N is perpendicular I believe the slope should be the opposite of M's, and it says it passes through the origin so I believe its intercept is 0 so i re wrote line N: to Y=4x + 0

the only point where these two lines share is there intersection where line M=N

-4x+k = 4x+0
k = 8x

x= k/8

plug into either equation to solve for Y = K/2

intersection point is K/8, K/2

since this is equal to P, k/8= R and K/2 = r+1

I think I must have made a mistake because after this point I get various answers that are wrong.

K/8 = K/2 + 1

I solve for K = - 8/3

then I plug back in to solve for R given R= k/8 thus

-8/3 divided by 8

and I get -1/3 = r

an exact difference of positive one... what did i do wrong?

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06 Mar 2012, 12:01
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In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

The equation of line m is y=-4x+k. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.

Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.

For more on this subject check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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07 Mar 2012, 03:05
Thanks a lot

I was stuck at that point, that k=o, because passing through the origin

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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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29 May 2013, 07:36
Bumping for review and further discussion.
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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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30 May 2013, 23:39
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newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!

You can approach by calculating slopes of both lines m and n.

As we know both m and n lines are perpendicular; slope m* slope n= -1

slope of m= -4 since 4x=y+k =>(Y=mx+c), where m is slope

now calculate slope of n. as we know line passes through origin (0,0) and (r, r+1)

slope = (y2-y1)/(x2-x1) => (r+1-0)/(r-0) => (r+1)/r

lines are perpendicular; thus we can multiply both slopes

(r+1)/r*-4=-1 gives r= -4/3

Hence Ans is A.

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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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06 Dec 2015, 05:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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06 Dec 2015, 05:24
newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!

Two perpendicular lines with slopes m1 and m2 are such that m1*m2 = -1

Given that lines m and n are perpendicular to each other ---> slope of n = -1/slope of line m = -1/-4 = 1/4

Also, line n passes through (0,0) ---> y = ax+b ---> b=0 and a =1/4 --> equation of line n = y =x/4

Now as point (r,r+1) lies on n , substitute y=r+1 and x=r --> 4(r+1)=r --> 4r+4 = r --> 3r=-4 --> r = -4/3.. A is the correct answer.
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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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07 Dec 2015, 06:43
newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Given:
Line m: 4x + y = k Or y = -4x + k
Line n passes through (0,0) and is perpendicular to line m

If two lines are perpendicular, then the product of their slopes = -1

Hence slope of line n = 1/4

Equation of line n:
y - 0 = 1/4(x-0)
y = x/4

Point p lies on the line n
Hence: r+1 = r/4,
4r + 4 = r
r = -4/3
Option A
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Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

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15 Mar 2017, 07:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In the xy plane line m has the equation 4x + y = k. Line n   [#permalink] 15 Mar 2017, 07:05
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