Question

Fuzzy draws a segment of positive length in a plane. How many locations can Fuzzy place another point in the same plane to form a non-degenerate isosceles right triangle with vertices consisting of his new point and the endpoints of the segment?

Answer 1

Answer: 2 locations.

Explanation:

A non-degenerate triangle means that the 3 vertices are no colinear, so we can not draw the other point in top of the segment.

Now, if we want to construct an isosceles triangle, then we must start for the middle of the segment, now we draw a line that cuts perpendicularly our segment by that point (by the middle).

Now, any point in that line is at the same distance from both ends of our triangle.

now the angle between those two new sides must be 90°, (because this is a right triangle) so we have, for each side of our segment, a unique location such that the end result is a non-degenerate isosceles triangle.

So we have 2 locations