JEE Main 2022 · 29 Jun · Shift 2 · Mathematics Q13

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MathematicsSingle correct+4 / -1Question 13 of 90

The distance of the origin from the centroid of the triangle whose two sides have the equations $x-2y+1=0$ and $2x-y-1=0$ and whose orthocenter is $\left(\dfrac73,\dfrac73\right)$ is:

\sqrt2

2\sqrt2

Answer and worked solution

Official answer: C

Vertex A $=(1,1)$ where the two sides meet. Using the orthocentre H: B on $x-2y+1=0$ with $BH\perp$ the other side gives $B=(3,2)$ ; similarly $C=(2,3)$ .

Centroid $(2,2)$ , distance $2\sqrt2$ .

(C)

Topics:Equations of a line Distance and section formulae

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JEE Main 2022 · 29 Jun · Shift 2, Mathematics question 13