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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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Difficulty:

45% (medium)

Question Stats:

73% (02:54) correct
27% (01:50) wrong based on 83 sessions

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)?

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

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 _________________

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.

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 \((4,9)\).

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....

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

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