JEE Main 2023MathematicsStraight LinesHardMCQ

JEE Main 2023 — Straight Lines Question with Solution

JEE Main 2023 (29 Jan Shift 1)

Question

Let B and C be the two points on the line y+x=0 such that B and C are symmetric with respect to the origin. Suppose A is a point on y-2x=2 such that ∆ABC is an equilateral triangle. Then, the area of the ∆ABC is

Choose an option

Show full solutionCorrect option: C
Correct answer
C83

Step-by-step explanation

On plotting the diagram of the given data we get,

Now given, x=y and y-2x=2

On solving we get, A(-2,-2)

Now height h of ∆ABC = Distance of point A to origin,

h=-22+(-2)2

⇒h=22

Given ∆ABC is an equilateral triangle,

So, sinB=hAB

⇒sin60°=hAB   (∵∠A=∠B=∠C=60°)

Area of Δ=34AB2

⇒Area of Δ=34h2sin260∘=34×323

So, Area of ∆ABC=83

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About this question

This is a previous-year question from JEE Main 2023, covering the Straight Lines chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.