JEE Main 2018MathematicsProperties of TrianglesHardMCQ

JEE Main 2018 — Properties of Triangles Question with Solution

JEE Main 2018 (15 Apr)

Question

In a triangle ABC, coordinates of A are 1, 2 and the equations of the medians through B and C are respectively, x+y=5 and x=4. Then area of ΔABC (in sq. units) is :

Choose an option

Show full solutionCorrect option: C
Correct answer
C9

Step-by-step explanation

Let C4, α be on x=4.

Now, midpoint of AC is 52, α+22 which lies on x+y=5.

∴α+22=52⇒α=3

∴C4, 3

Similarly, let Bβ, 5-β be on x+y=5.

The midpoint of AB =β+12, 7-β2 which lies on x=4⇒β=7⇒B7, -2.

   

∴ Area of Δ=121217-21431

=121-2-3-27-4+121+8=1218=9 sq. units

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About this question

This is a previous-year question from JEE Main 2018, covering the Properties of Triangles 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.