JEE Main 2017MathematicsStraight LinesMediumMCQ

JEE Main 2017 — Straight Lines Question with Solution

JEE Main 2017 (02 Apr)

Question

Let k be an integer such that the triangle with vertices k,-3k, 5, k and -k, 2 has area 28 sq. units. Then the orthocenter of this triangle is at the point:

Choose an option

Show full solutionCorrect option: D
Correct answer
D2,12

Step-by-step explanation

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Given, Area of the triangle ∆ABC=28⇒12kk-2+52+3k-k-4k=28

⇒kk-2+52+3k-k-4k=56

⇒ 5k2+13k−46=0

⇒ k=2 and k=-235 (Not possible)

Altitude from  A : x=2

Altitude from B : y-2=12x-5

So, their point of intersection is H2,12

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About this question

This is a previous-year question from JEE Main 2017, 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.