Mathematics - Point Question with Solution | TestHub

Let$A\left(1,0\right),B\left(6,2\right)$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