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

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In the xy-coordinate system, what is the slope of the line [#permalink]  03 Apr 2008, 15:06
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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)?
2
2.25
2.50
2.75
3
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CEO
Joined: 17 Nov 2007
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Concentration: Entrepreneurship, Other
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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.
CEO
Joined: 17 Nov 2007
Posts: 3600
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Re: PS: Line [#permalink]  04 Apr 2008, 21:12
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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Re: PS: Line [#permalink]  04 Apr 2008, 21:32
walker wrote:
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

Very good...
thnx for expln
Re: PS: Line   [#permalink] 04 Apr 2008, 21:32
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