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In a rectangular coordinate system ............

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by pzazz12 » Tue Oct 19, 2010 11:43 pm
In a rectangular coordinate system ,which of the following points is intersected by the line connected by the coordinates (5,6) and(21,18)?

A.(9,9)
B.(12,12)
C.(13,13)
D.(12,13)
E.(16,15)
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by Rahul@gurome » Wed Oct 20, 2010 12:48 am
We first find out the equation of line connecting (5,6) and (21, 18) and then verify which of the given points satisfy the equation.
Let the equation of line be y = mx + c.
So 6 = 5m + c and 18 = 21m + c.
Solving we get that m = ¾ and c = 9/4.
Or equation of line is y = 3/4x + 9/4.
Only (9,9) satisfies the above equation.
The correct answer is A.
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by fskilnik@GMATH » Wed Oct 20, 2010 3:19 am
Rahul@gurome wrote:We first find out the equation of line connecting (5,6) and (21, 18) and then verify which of the given points satisfy the equation.
Let the equation of line be y = mx + c.
So 6 = 5m + c and 18 = 21m + c.
Solving we get that m = ¾ and c = 9/4.
Or equation of line is y = 3/4x + 9/4.
Only (9,9) satisfies the above equation.
The correct answer is A.
It is a pleasure to read Rahul´s solutions and I strongly advise the GMAT candidates to study them carefully.

Just to prove that I also read it with attention :) , I would like to add that to guarantee the point we are looking for is in the line segment with (5,6) and (21,18) as extremities, I would just mentioned that the x-coordinate should be between 5 and 21 or, equivalently, that the y-coordinate should be between 6 and 18. (It is the case, for sure.)

Regards,
Fabio.
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by swutherton » Wed Oct 20, 2010 11:10 am
Agreed with both the posts above, but I have a suggestion:

A quicker way of doing this would be to just go for slope= (Y2-Y1) / (X2-X1), so you dont have to build the equation.
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by SubodhChawla » Tue Jul 19, 2011 12:21 pm
I really like the method that's shown here.

I took a completely different approach, it may be faster but may not be 100% accurate every single time. It primarily depends on the format in which the options are given.

I found the mid point of the line (5,6) and (21,18), which came out to be (13,12). Thus eliminated B,C,D as all of them are very close but miss this point.

I than found out the mid point of (5,6) and (13,12) that comes out to be (9,9) which is option A.
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by hagan » Tue Jul 19, 2011 3:51 pm
very helpful tips, thanks to the team on this forum.
i want to know it all i am ready to learn it all
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