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Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol
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30 Oct 2014, 08:38
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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
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol
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25 Nov 2015, 03:28
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.
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol
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25 Nov 2015, 07:45
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.
Re: Line L contains the points (2,3) and (p,q). If q = 2, which of the fol
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19 Sep 2018, 15:53
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