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

Question

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 (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P is centroid of the triangle ABC ⇒ P ≡ ((17/6), (8/3)) ⇒ PQ = 5

Q. Let A (1, 0), B(6, 2) and C(23​,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 (−67​,−31​), is _________ . Given 5

P is centroid of the triangle ABC ⇒P≡(617​,38​) ⇒PQ=5

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