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.
In a rectangular coordinate system ............
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Rahul@gurome
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fskilnik@GMATH
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It is a pleasure to read Rahul´s solutions and I strongly advise the GMAT candidates to study them carefully.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.
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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swutherton
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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.
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.
Accepted into Haas, Kellogg, Duke, INSEAD, Wharton, Michigan 6/6
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SubodhChawla
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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.
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.
