perplexus.info :: Just Math : A Square in the First Quadrant

A Square in the First Quadrant (Posted on 2024-08-31)

Given a square ABCD with two consecutive vertices, say A and B on the positive x-axis and positive y-axis respectively. Suppose the other vertex C lying in the first quadrant has coordinates (u , v). Then find the area of the square ABCD in terms of u and v.

No Solution Yet Submitted by Danish Ahmed Khan

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soln

| Comment 1 of 2

If I understand correctly, for a square side s,

A=(sqrt2 s/2, 0), B=(0, sqrt2 s/2), C=(u,v)=(sqrt2 s/2, sqrt2 s),

so, Area = s^2 = v^2/2 and Area= 2 u^2 and Area = uv

Later: This is wrong as I assumed A and B equidistant from the origin. I knew it looked too easy!

Edited on September 1, 2024, 12:20 am

Posted by Steven Lord on 2024-08-31 16:34:07

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