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
The solution provided to this involves finding the all the possible integer coordinates of the other vertex side whose first is at origin (resulting in a length of 10). [-8,-6 -10,0 etc.]. However, implicit in the solution is the assumption that if these two vertices are made of integers, the others will be as well. This isn't obvious to me.
Could some shed some clarity on why that must be true?
Thanks, guys
Arnav
A) 4
B) 6
C) 8
D) 10
E) 12
The solution provided to this involves finding the all the possible integer coordinates of the other vertex side whose first is at origin (resulting in a length of 10). [-8,-6 -10,0 etc.]. However, implicit in the solution is the assumption that if these two vertices are made of integers, the others will be as well. This isn't obvious to me.
Could some shed some clarity on why that must be true?
Thanks, guys
Arnav
