JEE Main 2020MathematicsStraight LinesMediumMCQ

JEE Main 2020 — Straight Lines Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

A triangle ABC lying in the first quadrant has two vertices as A1,2 and B3,1. If∠BAC=90o,and arΔABC=55 sq. units, then the abscissa of the vertex C is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B1+25 

Step-by-step explanation

mAC=β−2α−1

mAB=2−11−3=−12

AB⊥AC

∴ β−2α−1−12=−1

β=2α−2+2

β=2α

Now area of ΔABC=55=12AB.AC

⇒ 123−12+1−22.α−12+β−22=55

⇒ α−12+2α−22=10

⇒ α−125=10

⇒ α−1=25

⇒ α=1±25.

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About this question

This is a previous-year question from JEE Main 2020, 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.