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I think only 4 squares with area 100 are possible. When you make the additional 4 squares by drawing a line at 45 degree angle, you change the side of the square from 10 to sqrt 200, which will not give you the area 100 (which is what the question is asking).adi_800 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
square will have an area of 100, if the side length is 10adi_800 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
"One of the vertices must be on the origin" - I understand this as a requirement that one of the corners of the square has to be on 0. But the points (8,6) for example, doesnt meet that requirement.gmatmachoman wrote:coordinates are :
Following are the starting point(base) of the squares that can be formed.
(10,0)
(-10,0)
(0,10)
(0,-10)
(8,6)
(-8,6)
(8,-6)
(-8,-6)
(6,8)
(6,-8)
(-6,8)
(-6,-8)
So 12 squares can be formed....
The attached .pdf shows the 12 squares that can be formed. Each square satisfies the conditions of the problem:beatthegmatinsept wrote:"One of the vertices must be on the origin" - I understand this as a requirement that one of the corners of the square has to be on 0. But the points (8,6) for example, doesnt meet that requirement.gmatmachoman wrote:coordinates are :
Following are the starting point(base) of the squares that can be formed.
(10,0)
(-10,0)
(0,10)
(0,-10)
(8,6)
(-8,6)
(8,-6)
(-8,-6)
(6,8)
(6,-8)
(-6,8)
(-6,-8)
So 12 squares can be formed....
What am I missing here?
GMATGuruNY wrote:The attached .pdf shows the 12 squares that can be formed. Each square satisfies the conditions of the problem:beatthegmatinsept wrote:"One of the vertices must be on the origin" - I understand this as a requirement that one of the corners of the square has to be on 0. But the points (8,6) for example, doesnt meet that requirement.gmatmachoman wrote:coordinates are :
Following are the starting point(base) of the squares that can be formed.
(10,0)
(-10,0)
(0,10)
(0,-10)
(8,6)
(-8,6)
(8,-6)
(-8,-6)
(6,8)
(6,-8)
(-6,8)
(-6,-8)
So 12 squares can be formed....
What am I missing here?
-- one vertex is at the origin
-- the area of each square is 100
-- the coordinates of each vertex are integers
Hope this helps!
Here are the conditions:praveen_gmat wrote:GMATGuruNY wrote:The attached .pdf shows the 12 squares that can be formed. Each square satisfies the conditions of the problem:beatthegmatinsept wrote:"One of the vertices must be on the origin" - I understand this as a requirement that one of the corners of the square has to be on 0. But the points (8,6) for example, doesnt meet that requirement.gmatmachoman wrote:coordinates are :
Following are the starting point(base) of the squares that can be formed.
(10,0)
(-10,0)
(0,10)
(0,-10)
(8,6)
(-8,6)
(8,-6)
(-8,-6)
(6,8)
(6,-8)
(-6,8)
(-6,-8)
So 12 squares can be formed....
What am I missing here?
-- one vertex is at the origin
-- the area of each square is 100
-- the coordinates of each vertex are integers
Hope this helps!
Hey GMATGuruNY,
Thanks for the answer... But how do I approach the problem? How to solve it quickly?
