Hard MGMAT 700-800 level question. Co-ordinate plane

sarang_gmt11 wrote:

GMATGuruNY wrote:

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
A)4
B)6
C)8
D)10
E)12

Step 1: If area = 100, side = 10.
Step 2: Recognize that the hypotenuse of a 6-8-10 triangle is 10.
Step 3: Plot coordinate pairs using every possible combination of (±6,±8), (±8,±6),(0,±10) and (±10,0).
Step 4: Using the plotted points, draw sets of squares centered about the origin. The following sets are possible:



Number of possible squares = 12.

The correct answer is E.

Hi ,
In the above diagram you have shown the centre of the square on the origin but in the problem it is mentioned that one of the vertices must be on the origin ?

imhimanshu wrote:Sorry to bring up the old post..but somehow I am not able to get the solution.. request you to please clarify my below doubts -

1- I understand that we are employing Pythagorean triplets, but I am not been able to follow how that triplets will help me in solving/understanding that all other points will be integer.
Please explain

GMATGuruNY wrote:

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?
A)4
B)6
C)8
D)10
E)12

Step 1: If area = 100, side = 10.
Step 2: Recognize that the hypotenuse of a 6-8-10 triangle is 10.
Step 3: Plot coordinate pairs using every possible combination of (±6,±8), (±8,±6),(0,±10) and (±10,0).
Step 4: Using the plotted points, draw sets of squares centered about the origin. The following sets are possible:



Number of possible squares = 12.

The correct answer is E.