JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q80

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MathematicsSingle correct+4 / -1Question 80 of 90

Given three points P, Q, R with P(5, 3) and R lies on the $x$ -axis. If equation of RQ is $x-2y=2$ and PQ is parallel to the $x$ -axis, then the centroid of $\Delta PQR$ lies on the line :

2x+y-9=0

x-2y+1=0

5x-2y=0

2x-5y=0

Answer and worked solution

Official answer: D

Q is on $y=3$ and on $x-2y=2$ : $Q(8,3)$ .
R is on the $x$ -axis and on RQ: $R(2,0)$ .
Centroid: $\left(\frac{5+8+2}3,\frac{3+3+0}3\right)=(5,2)$ , which satisfies $2x-5y=0$ .

Topics:Equations of a line Distance and section formulae

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 80