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# M15#19

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Joined: 12 Sep 2010
Posts: 223
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08 May 2012, 15:59
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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?
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09 May 2012, 03:17
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, 03:17
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# M15#19

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