First slide

Cartesian plane

Question

Let A(1, 0), B(6, 2) and $C (\frac{3}{2}, 6)$ be the vertices of a triangle ABC. If P is a point inside the $Δ A B C$ such that $Δ A P C, Δ A P B & Δ B P C$ have equal areas, then the length of the line segment PQ, where Q is the point $(- \frac{7}{6}, - \frac{1}{3})$ is_____.

Easy

Solution

P must be centroid of $Δ A B C$
$\Rightarrow P (\frac{17}{6}, \frac{8}{3}) ∴ P Q = \sqrt{{(\frac{24}{6})}^{2} + (\frac{9}{3})} = 5$

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