A point moves on the line . If and are fixed points, then the locus of the centroid of is a line:

Question

A point  moves on the line . If  and  are fixed points, then the locus of the centroid of  is a line:

Canvas Classes · Accepted Answer

🧠 Centroid Inherits the Slope of the Parametrised Vertex

If two vertices are fixed and one () moves along a line, the centroid traces a line parallel to that line — but scaled by . So the centroid's locus has the SAME slope as the line  moves on, namely the slope of , which is .

🗺️ The Clean Algebraic Route

Let  with . Centroid:

, .

So . Sub into the line equation:

.

Slope: .

⚡ The 30-Second Move

Centroid is a linear (affine) function of . Linear maps preserve slopes (for parallel lin

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