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JEE Main 20207 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2020 · 7 January · Morning Shift · Mathematics · Straight Lines

Let A (1, 0), B (6, 2) and C((3)/(2), 6) be the vertices of a...

Let A(1,0),B\left(1, 0\right), B\left(6, 2\right)andandC(32,6)C\left(\dfrac{3}{2}, 6\right) be the vertices of a triangle ABC.ABC . If PP is a point inside the triangle ABCABC such that the triangles APC,APBandBPCAPC, APB and BPC have equal areas, then the length of the line segment PQ,PQ, where QQ is the point (−76,−13),\left(- \dfrac{7}{6}, - \dfrac{1}{3}\right), is

Correct answer

5

Step-by-step solution

PP must be centroid of ∆ABC∆ ABC
∴P(176,83)⇒PQ=(246)2+(93)=5∴ P\left(\dfrac{17}{6}, \dfrac{8}{3}\right) ⇒ PQ = \sqrt{{\left(\dfrac{24}{6}\right)}^{2} + \left(\dfrac{9}{3}\right)} = 5 units
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