Use coordinates, distance, and algebra to prove or disprove simple geometric statements.
Use coordinates to prove a segment is a median
Problem
For triangle \(A(0,4)\), \(B(-2,0)\), \(C(6,0)\), test whether \(AM\) with \(M(2,0)\) is a median. Calculate the midpoint of \(BC\), compare it with \(M\), and state the conclusion.
Start from the definition: a median must join a vertex to the midpoint of the opposite side, not merely to some point on that side. Identify the opposite side, average its endpoint coordinates independently, and compare both resulting coordinates with the proposed endpoint before classifying the segment.
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