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M15#19

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M15#19 [#permalink] New post 08 May 2012, 14:59
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If on the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square, what is the distance between point (0, 0) and the closest vertex of the square?

A \frac{1}{\sqrt{2}}
B 1
C \sqrt{2}
D \sqrt{3}
E 2\sqrt{3}

Official Explanation:
First, we have to "guess" the coordinates of the vertex of the square closest to the origin. We can do it by making a sketch. The coordinates of the vertex are (1, 1) and it is \sqrt{2} units away from the origin.

When you make "sketch", how can you be sure that the diagonal of the square is perpendicular to the origin?
[Reveal] Spoiler: OA
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Re: M15#19 [#permalink] New post 09 May 2012, 02:17
Expert's post
Samwong wrote:
If on the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square, what is the distance between point (0, 0) and the closest vertex of the square?

A \frac{1}{\sqrt{2}}
B 1
C \sqrt{2}
D \sqrt{3}
E 2\sqrt{3}

Official Explanation:
First, we have to "guess" the coordinates of the vertex of the square closest to the origin. We can do it by making a sketch. The coordinates of the vertex are (1, 1) and it is \sqrt{2} units away from the origin.

When you make "sketch", how can you be sure that the diagonal of the square is perpendicular to the origin?


Discussed here: coordinate-plane-90772.html

Check this solution: coordinate-plane-90772-60.html#p692465

Hope it helps.
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Re: M15#19   [#permalink] 09 May 2012, 02:17
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