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A certain square is to be drawn on a coordinate plane. One [#permalink]
27 Mar 2013, 21:40

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 Need help

Re: A certain square is to be drawn on a coordinate plane. One [#permalink]
27 Mar 2013, 22:06

Perimeter of a circle of radius 10 centered at the origin will coincide with 12 points where where both the x and y values are integers. (10, 0); (8, 6); (6, 8); (0, 10); (-8, 6), (-6, 8); (-10, 0); (-8, -6); (-6, -8); (0, -10); (8, -6); (6, -8)

Re: A certain square is to be drawn on a coordinate plane. One [#permalink]
28 Mar 2013, 02:04

Expert's post

mun23 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 Need help

Re: A certain square is to be drawn on a coordinate plane [#permalink]
28 Apr 2013, 08:55

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?

Doesn't one of the vertices must be on the origin mean one vertices of the square has always to be (0,0) hence only 4 possibilities ??? Please clarify !!

Re: A certain square is to be drawn on a coordinate plane [#permalink]
28 Apr 2013, 19:50

karishmatandon wrote:

Since area of the square is 100, each side = 10 One of the vertices of the square = (0,0) Let the co-ordinates of another vertex of the square be (x,y) Using the formula d^2 = x^2 + y^2 (d = Distance from the origin to any point in the co-ordinate) So, 100 = x^2 + y^2 As the vertices, must be integers, solve for different values for x and y When x = 0, y = 10 Also, x = 0, y = -10 x=10, y = 0 x = -10, y = 0 Also x = 6 , y = 8 (as 100 = 6^2+8^2) x = 6, y = -8 x = -6, y= 8 x = -6, y = -8 Similarly, x = 8, y = 6 x = 8, y = -6 x = -8, y = 6 x = -8, y = -6

that is 12 possible values

This diagram posted earlier in the forum explains everything

Re: A certain square is to be drawn on a coordinate plane [#permalink]
29 Dec 2013, 01:16

Got this question wrong on the mgmat cat also.

What I still don't understand how you confirm that a square that has a hypotenuse as an edge running from 0,0 to 6,8, would also have vertices at integer co-ordinates 8,6, and 14,2 and not fractional co-ordinates. How do you reach that conclusion?

gmatclubot

Re: A certain square is to be drawn on a coordinate plane
[#permalink]
29 Dec 2013, 01:16