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  4. Let A (1, 0), B(6, 2) and C((3/2), 6) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point (-(7/6), -(1/3)), is . Given 5

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Q. Let A (1, 0), B(6, 2) and C$\left(\frac{3}{2}, 6\right)$ be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point $\left(-\frac{7}{6}, -\frac{1}{3}\right),$ is _________ .
Given 5

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Solution:

P is centroid of the triangle ABC
$\Rightarrow P \equiv \left(\frac{17}{6}, \frac{8}{3}\right)$
$\Rightarrow PQ = 5$