A Square is to be drawn on the xy-plane. If one vertex of the square

Hi,

This is a very interesting question.

Easily someone could fall for the trap answer as 4 here.

If one visualize the squares only on the x and y axis, then they end up falling for the trap.

So the vertices need not be only on the x and y axis, they have mentioned all the vertices should be integers,

So, Let’s try to visualize it,

We can see that,

Co-ordinates (-4,3) forms a side length of the square as 5 from the origin (0,0), Because 3-4-5 are pythogorean triplets.

As shown in the figure(In the attachment), we can form four squares starting with point (-4,3).

So similarly starting with the point (-3,4), we can form 4 different squares.

Already on the x and y axis there are 4 different squares.

So totally, we can form 12 different squares with side length as 5 and one vertex at the origin. So the answer is D.

Most important factor of solving a co-ordinate geometry question is visualizing.

Hope this helps.