smclean23 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?
4
6
8
10
12

i go with D 12.

here it goes

we know one of the vertices is @origin (0,0)
let the other vertice be @ (x,y)

now use the distance formula

(x-0)^2 + (y-0)^2 = 100
X^2 +Y^2 = 10^2

thus the coordinates can be (0,10) ,(10,0), (8,6) and ( 6,8)

but in this both ( 0,10) and (10,0) lie on the same quadrant. hence we have 3 vertices and 4 quadrants

thus the total number of squares are 3*4 = 12

hope it helps..
do let me know if u have any doubts..