Let A ( 1 , 0 ) , B ( 6 , 2 ) and C ( 3 2 , 6 ) be the vertices of a triangle A B C . If P is a point inside the triangle A B C such that the triangles A P C , A P B and B P C have equal areas, then the length of the line segment P Q

Question

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

Smart Achievers · Accepted Answer

(5)

$Since, ar (∆ P A B) = ar (∆ P A C) = ar (∆ P B C)$ $[Given]$

$A B C$ $P will be centroid of ∆ A B C .$

$So, coordinates of P are$ $(\frac{17}{6}, \frac{8}{3}) .$

$Now,$ $P Q = \sqrt{{(\frac{24}{6})}^{2} + {(\frac{9}{3})}^{2}} = 5$

Solution

Ans.
(5)

$Since, ar (∆ P A B) = ar (∆ P A C) = ar (∆ P B C)$ $[Given]$

$∴$ $P will be centroid of ∆ A B C .$

$So, coordinates of P are$ $(\frac{17}{6}, \frac{8}{3}) .$

$Now,$ $P Q = \sqrt{{(\frac{24}{6})}^{2} + {(\frac{9}{3})}^{2}} = 5$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Let A(1, 0), B(6, 2) and C(32,6) 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 (-76,-13), is ________.

Ans. (5) Since, ar(∆PAB)=ar(∆PAC)=ar(∆PBC) [Given] ∴ P will be centroid of ∆ABC. So, coordinates of P are (176,83). Now, PQ=(246)2+(93)2=5

Want Us to Email you About Special Offers & Updates?

Ans.
(5)

$Since, ar (∆ P A B) = ar (∆ P A C) = ar (∆ P B C)$ $[Given]$

$∴$ $P will be centroid of ∆ A B C .$

$So, coordinates of P are$ $(\frac{17}{6}, \frac{8}{3}) .$

$Now,$ $P Q = \sqrt{{(\frac{24}{6})}^{2} + {(\frac{9}{3})}^{2}} = 5$