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📰 Question: A herpetologist tracks the movement of a rare frog across a triangular habitat with vertices at $(1,2)$, $(4,6)$, and $(7,2)$. If the frog is at the centroid of this triangle and then moves to a point equidistant from all three vertices, find the minimum distance it must travel to reach such a point.
📰 Solution: First, find the centroid $G$ of the triangle with vertices $A(1,2)$, $B(4,6)$, $C(7,2)$. The centroid is:
📰 To $C(7,2)$: same by symmetry, so we use $B(4,6)$:
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