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Which of the following coordinates are on the line segment

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Intern
Joined: 30 Oct 2005
Posts: 19
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Which of the following coordinates are on the line segment [#permalink]  05 Nov 2005, 14:53
Which of the following coordinates are on the line segment connecting (5,6) and (21,18)?

A) (9,9)

B) (12,12)

C) (13,13)

D) (12,13)

E) (16,15)
Manager
Joined: 04 Oct 2005
Posts: 246
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[#permalink]  05 Nov 2005, 15:53
If three points are on the same line segment, than each of the point should have the same slope with either of the other.
Slope of the points from the stem:
(18-6)/(21-5)=12/16=3/4

so let's try the answers. Take (5,6) because the numbers will be lower and thus easier to calculate with:

A) (9-6)/(9-5)=3/4 wow, that seems like our candidate...
Lets check B as well, just to be sure
B) (12-6)/(12-5)=6/7 ... different slope so the point will not be on that linesegment.

there is no need to calculate any further, so we save time
Intern
Joined: 30 Oct 2005
Posts: 19
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[#permalink]  09 Nov 2005, 17:33
Nero44 - correct and very elegant. OA is indeed A.
[#permalink] 09 Nov 2005, 17:33
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Which of the following coordinates are on the line segment

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