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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?

I get 8 as well. By drawing 1 big square from 4 little squares resting on the axis. Then I get another big square that has the diagonals of each square resting on an axis.

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

I get 8 (C). Two different ways in each of the four regions.

oh shoot.. I think this is a trick question. I change my answer to A (4) because if the set of four squares drawn diagonally cannot generate non-integer coordinates (hence (0, 10sqrt2), etc) we cannot consider those!

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 think its A, just because it is a square with area 100, so each side must be 10, it cannot be any other shape than a 10x10 square. so if this is the case, then it can only be drawn four ways, one in each quadrant bc the origin (0,0) has to be one of the vertices. unless I am missing something...

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

12

one vertice must be on (0,0) each quadrant find how many points (integer points which makes the line with side 10 ) (0,10) , (8,6), (6,8).. So you can draw 3 squares in each quadrant .

Answer 4*3=12

Figure is on the way

Attachments

sqrs.gif [ 4.08 KiB | Viewed 985 times ]

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yes that makes a lot of sense, I guess you could just kind of figure out which numbers squared equals 10 squared, which are 8 and 6. I assume this is like an 800 level question?

Re: Number of squares [#permalink]
14 Sep 2008, 14:44

pallavi79us 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 Please explain how you arrive at a solution. OA will follow.

thanks,

We need to find out coordinates such that the distance between (0,0) and (x,y) is 10 (since area is 100, side =10)

(0,0) (10,0) 4 such squares in 4 Quadrants

(0,0) (8,6) 4 such squares (8,-6) ( -8,6) (-8,-6)

(0,0) (6,8) 4 such squares (6,-8) (-6,8) and (-6,-8)

For co-ordinates to be integers, possible co-ordinates for one of the vertices are (6,8), (8,6), (10,0) in one quadrant. Multiply this number of three different co-ordinates with four quadrants....and hence the answer should be 12.

Geometry Question - need help [#permalink]
04 Feb 2009, 07:00

I've been having a hard time understanding the solution to this problem. Can anyone offer a simple explanation? Thanks in advance.

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?

Re: Geometry Question - need help [#permalink]
04 Feb 2009, 08:11

srpradhan wrote:

I've been having a hard time understanding the solution to this problem. Can anyone offer a simple explanation? Thanks in advance.

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?

***The Answer is 12 but I don't understand why.

Look for the clue: If all coordinates of the vertices must be integers.

How is a squre with area 100 possible? If its sides are each 10. How is a side with 10 is possible subject to the coordinates that make the the side 10? Its possible only with 6 abd 8 coordinates. So possibilities are:

first qd: i: 10 and 0 ii: 8 and 6 ii: 6 and 8

Second qd: i: 0 and 10 ii: -6 and 8 ii: -8 and 6

similarly there are 3 more in each of 3rd and 4th quadrant.