JEE Main 2020 (Online) 7th January Morning ShiftQuestion 1
Let $A(1,0)$, $B(6,2)$ and $C\left(\frac32,6\right)$ 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 $\left(-\frac76,-\frac13\right)$, is
Points and Straight Lines
Answer$5$
Solution
Equal areas make $P$ the centroid $\left(\frac{17}{6},\frac83\right)$; $PQ=\sqrt{4^2+3^2}=5$.