Agreed!

Explain why the following statement is false: “In space, the perpendicular bisector of a line segment is unique.”

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Answer:

In a 2-dimensional plane there is only one line that is perpendicular to another. This follows from the fact that a straight line is uniquely defined by its slope and a point it passes through if there a constraint is imposed that they lie in the same plane.

On the other hand in 3-dimensional space, the number of lines that are perpendicular to a line and pass through its mid-point is not restricted. In 3 dimensional space there are an infinite number of lines that can pass through the mid-point of a line and which are also perpendicular to it.

As a result the statement "In space, the perpendicular bisector of a line segment is unique." is false.

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