Straight LineHardBloom L3
Question
If the vertices $P$ and $Q$ of a triangle $PQR$ are given by $(2,5)$ and $(4, - 11)$ respectively, and the point $R$ moves along the line $N:9x + 7y + 4 = 0$, then the locus of the centroid of the triangle $PQR$ is a straight line parallel to :
Options
A.$PQ$
B.$QR$
C.$RP$
D.$N$
Solution
Sol. [Key Concept: The centroid's locus is a line parallel to the path of the moving vertex.]
$$R \equiv (3h - 6,3k + 6) $$
$R$ lies on $9x + 7y + 4 = 0$.
$${\Rightarrow 9(3h - 6) + 7(3k + 6) + 4 = 0 }{\Rightarrow (9h + 7k)3 - 8 = 0 }$$Which is parallel to $N$.
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