SOLUTION: If the sum of the distances of a point from two perpendicular lines in a plane is 1, then what is its locus? Square is the ans

Question 946466: If the sum of the distances of a point from two perpendicular lines in a plane is 1, then what is its locus?
Square is the ans
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the x and y axes be the two perpendicular lines.
Then the distance from the origin will be the distance from the perpendicular lines.
So then the sum of the distances would be .
So in the first quadrant, the locus of points would look like a straight line with points (0,1) and (1,0).
In the second quadrant it would contain (0,1) and (-1,0).
Third quadrant (-1,0) and (0,-1).
and finally in the fourth quadrant (0,-1) and (1,0).
When you put it all together, it would be a square rotated 45 degrees about the origin, the length of the side of the square would be .

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