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

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.

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.

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.

very helpful tips, thanks to the team on this forum.