JEE MAIN - Mathematics (2020 - 7th January Morning Slot - No. 10)
Let A(1, 0), B(6, 2) and C $$\left( {{3 \over 2},6} \right)$$ 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 $$\left( { - {7 \over 6}, - {1 \over 3}} \right)$$, is ________.
Answer
5
Explanation
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P is centroid of the triangle ABC.
P = $$\left( {{{1 + 6 + {3 \over 2}} \over 3},{{0 + 2 + 6} \over 3}} \right)$$
= $$\left( {{{17} \over 6},{8 \over 3}} \right)$$
Given Q $$\left( { - {7 \over 6}, - {1 \over 3}} \right)$$.
$$ \therefore $$ PQ = $$\sqrt {{{\left( {{{24} \over 6}} \right)}^2} + {{\left( {{9 \over 3}} \right)}^2}} $$ = 5
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