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Math Challenge I-C Winter 2023 Geometry Problem 3.14

 
 
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Re: Math Challenge I-C Winter 2023 Geometry Problem 3.14
LensmireJohn - 2023年12月19日 Tuesday 12:40
 

Good question! It is always possible to try to graph and get a rough idea, but there is an important property that can also help:

  • If a line $\ell$ is the perpendicular bisector of $\overline{AB}$, then any point $C$ on the perpendicular bisector must be the same distance from $A$ as it is to $B$. If the distances are not equal, then $C$ is not on the perpendicular bisector.

This property is a nice way to check for this problem. Hope this helps!