Co-ordinate Geometry #3

[papgust]

If the co-ordinates of the mid-point of the line segment joining the points (2,1) and (1,-3) is (x,y) then the relation between x and y can be best described by

A. 3x+2y=5
B. 6x+y=8
C. 5x-2y=4
D. 2x-5y=4

Source: Arun Sharma's Quantitative Aptitude for CAT

Solution and explanation pls? I will give the OA after a few discussions

[crackgmat007]

To compute the coordinates of mid point take the average of x & y coordinates respectively

We get (3/2, -1). Plugging these values, B seems to be correct.

[Talkativetree]

crack is right, but I'll go a little bit more into the details about why. So if you plug the coordinates (2,1) and (1,-3) into a plane, you can create a triangle.

The triangles sides can be found by subtracting the x's and y's.

2-1=1
1-(-3)=4

NOW, don't try to figure out how long the hypotenuse is. because we simply need to find the midpoint, we draw a horizontal line from the halfway point of the hypotenuse, splitting the 1,4,x triangle into a smaller triangle. now, an understanding of the principles of triangles helps here, because we know that the smaller triangle we made is proportional to the larger triangle. because we know that it's hypotenuse is 1/2 the size of the larger triangles hypotenuse's, so then it's sides must then be 1/2, 2, and x/2.

with this, we at 1/2 to x and 2 to y.

x=1+1/2=3/2
y=-3+2=-1

NOW, cracks' method is much much quicker.

[papgust]

Thank you all. Got a bit confused by the line "relation between x and y can be best described as..". OA is indeed B.