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# Line L contains the points (2,3) and (p,q). If q = 2, which of the fol

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Math Expert
Joined: 02 Sep 2009
Posts: 50016
Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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29 Oct 2014, 08:34
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Difficulty:

55% (hard)

Question Stats:

69% (02:16) correct 31% (02:29) wrong based on 325 sessions

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Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7
(B) 2x + y = –px
(C) x + 2y = px + 7
(D) y – 7 = x ÷ (p – 2)
(E) 2x + y = 7 – px

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Manager
Joined: 21 Jul 2014
Posts: 126
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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30 Oct 2014, 09:38
6
3
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7
(B) 2x + y = –px
(C) x + 2y = px + 7
(D) y – 7 = x ÷ (p – 2)
(E) 2x + y = 7 – px

The image below shows the steps I took to solve the problem. Note, b as represented in the work shown below can equal any number since the problem does not specify where the perpendicular line M must cross with Line L.

Step by step:
1) Identify that we need to form the equation in a way to identify the slope (y = mx + b)
2) Identify the slope (m) using "rise over run", which is basically dividing the difference in y coordinates by the difference in x coordinates.
3) Find the slope of the perpendicular line (negative inverse of the first slope): m1
4) simplify the equation to match one of the answer choices
##### General Discussion
Director
Joined: 23 Jan 2013
Posts: 575
Schools: Cambridge'16
Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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24 Jul 2015, 05:57
we need m=p-2, so we should get "y=mx+b" form in answer choices

(A) 2x+y=px+7 => y=px-2x+7 => y=x(p-2)+7. It is what we need
(B) 2x + y = –px => y=-px-2x => y=x(-p-2). Wrong
(C) x + 2y = px + 7 => y=x(p-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (p – 2) => y=(1/p-2)x+7. Wrong
(E) 2x + y = 7 – px => y=-px-2x+7 => y=x(-p-2)+7. Wrong

A
Intern
Joined: 19 Apr 2015
Posts: 14
Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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25 Nov 2015, 01:42
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7
(B) 2x + y = –px
(C) x + 2y = px + 7
(D) y – 7 = x ÷ (p – 2)
(E) 2x + y = 7 – px

Hey Bunuel,

In the above solution instead of y=mx+c how can we get the solution using equation (y-y1)=m(x-x1),if not can you please elaborate why.
Senior Manager
Joined: 20 Aug 2015
Posts: 391
Location: India
GMAT 1: 760 Q50 V44
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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25 Nov 2015, 04:28
1
aby0007 wrote:
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7
(B) 2x + y = –px
(C) x + 2y = px + 7
(D) y – 7 = x ÷ (p – 2)
(E) 2x + y = 7 – px

Hey Bunuel,

In the above solution instead of y=mx+c how can we get the solution using equation (y-y1)=m(x-x1),if not can you please elaborate why.

Hi aby0007,

We surely can.
Let (x1, y1) = (2,3) and (x2, y2) = (p,q)
m = $$\frac{y2 - y1}{x2 - x1}$$ = $$\frac{q - 3}{p - 2}$$

Given q = 2
Therefore, m = $$\frac{-1}{p - 2}$$
This is the slope of the line L
We need to find the perpendicular line, hence the slope = p -2
Only Option A satisfies this.
Intern
Joined: 19 Apr 2015
Posts: 14
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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25 Nov 2015, 08:45
TeamGMATIFY wrote:
aby0007 wrote:
Bunuel wrote:

Tough and Tricky questions: Coordinate Geometry.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A) 2x + y = px + 7
(B) 2x + y = –px
(C) x + 2y = px + 7
(D) y – 7 = x ÷ (p – 2)
(E) 2x + y = 7 – px

Hey Bunuel,

In the above solution instead of y=mx+c how can we get the solution using equation (y-y1)=m(x-x1),if not can you please elaborate why.

Hi aby0007,

We surely can.
Let (x1, y1) = (2,3) and (x2, y2) = (p,q)
m = $$\frac{y2 - y1}{x2 - x1}$$ = $$\frac{q - 3}{p - 2}$$

Given q = 2
Therefore, m = $$\frac{-1}{p - 2}$$
This is the slope of the line L
We need to find the perpendicular line, hence the slope = p -2
Only Option A satisfies this.

Hey,

Sorry for not being clear I mean to say after finding the slope as (p-2).

When we are again putting values in y = mx +c can we use (y-y1)=m(x-x1); Thus giving us the required answer.

Thanks
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Joined: 09 Sep 2013
Posts: 8514
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol  [#permalink]

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19 Sep 2018, 16:53
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Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol &nbs [#permalink] 19 Sep 2018, 16:53
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