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In the xy-coordinate system, what is the slope of the line

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Senior Manager
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In the xy-coordinate system, what is the slope of the line [#permalink]  16 Jun 2007, 19:01
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In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

A. 2
B. 2.25
C. 2.50
D. 2.75
E. 3
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Jun 2014, 00:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: In the xy-coordinate system, what is the slope of the line [#permalink]  16 Jun 2007, 19:09
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Use midpoint formula to find point equidistant between P and Q; this point must be a part of our line: ((x1+x2)/2, (y1+y2)/2) = (4,9). Slope = rise/run = 9/4 = 2.25
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Re: PS: Line [#permalink]  03 Apr 2008, 16:04
Expert's post
B

line: y=ax

1. the line has to pass through the middle point (O) of the segment PQ.
2. the coordinates of the middle point are: (1+(7-1)/2, 7+(11-7)/2) = (4,9)
3. 9=a*4 --> a=2.25
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Re: PS: Line [#permalink]  04 Apr 2008, 19:10
walker wrote:
B

line: y=ax

1. the line has to pass through the middle point (O) of the segment PQ.
2. the coordinates of the middle point are: (1+(7-1)/2, 7+(11-7)/2) = (4,9)
3. 9=a*4 --> a=2.25

How can you assume that the line will pass through the mid point of PQ.
PQ may not be perpendicular to the line passing through origin.
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Re: PS: Line [#permalink]  04 Apr 2008, 21:12
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Expert's post
PM ┴ y=ax, QN ┴ y=ax

PM=QN, QNO=PMO=90°

angle POM = angle QON
angle OPM = angle OQN

So, ∆POM identical with ∆QON and PO=OQ
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What is the slope of the line that goes through the origin a [#permalink]  24 Mar 2011, 02:11
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What is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)?

A. 2
B. 2.25
C. 2.50
D. 2.75
E. 3
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Re: co ordinate geometry [#permalink]  24 Mar 2011, 02:29
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AnkitK wrote:
what is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)?
A.2
B.2.25
C.2.50
D.2.75
E.3

please provide some tips on co ordinate geometry or some usefull conceptual docs so that i could clear out the concepts of co ordinate geometry.

To get a slope of any line, we need at least 2 points that lie on line. We are already given that line passes through origin so one point is $$(0,0)$$.

Also, if p and q are equidistant from the line then the mid-point of line segment connecting P and Q lines on the given lines. Mid point is $$((7+1)/2, (11+7)/2)$$ or $$(4,9)$$.

So slope of line is $$(9-0)/(4-0) = 9/4 = 2.25$$.

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Re: co ordinate geometry [#permalink]  24 Mar 2011, 02:52
thnkxx beyondgmatscore.Also i was more interested in some theory concepts.
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Re: co ordinate geometry [#permalink]  24 Mar 2011, 05:00

math-coordinate-geometry-87652.html
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Re: co ordinate geometry [#permalink]  24 Mar 2011, 17:32
Expert's post
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AnkitK wrote:
thnkxx beyondgmatscore.Also i was more interested in some theory concepts.

Most co-ordinate geometry questions become way easier the moment you draw them out... the extra seconds almost always provide a lot of value... Knowing some basic formulas helps and you should be very efficient in drawing lines from their equations, from their slope and a point, from two points etc... Check out the links given below for some concepts on lines, slopes and points....

http://www.veritasprep.com/blog/2010/12 ... he-graphs/
http://www.veritasprep.com/blog/2010/12 ... s-part-ii/
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Re: co ordinate geometry [#permalink]  03 Jan 2013, 04:59
AnkitK wrote:

What is the slope of the line that goes through the origin and is equidistant from the two points p(1,11) and q(7,7)?
A.2
B.2.25
C.2.50
D.2.75
E.3

First, get the middle coordinate between (1,11) and (7,7)...
x = 1 + (7-1)/2 = 4
y = 7 + (11-7)/2 = 9

Second, get the slope of (4,9) and (0,0). m = 0-9 / 0-4 = 9/4 = 2.25

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Re: In the xy-coordinate system, what is the slope of the line [#permalink]  18 Jun 2014, 19:49
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