JEE Main 2016MathematicsStraight LinesMediumMCQ

JEE Main 2016 — Straight Lines Question with Solution

JEE Main 2016 (03 Apr)

Question

Two sides of a rhombus are along the lines, x-y+1=0 and 7x-y-5=0 . If its diagonals intersect at -1, -2 , then which one of the following is a vertex of this rhombus ?

Choose an option

Show full solutionCorrect option: A
Correct answer
A13, -83

Step-by-step explanation



d1 :y-2=-2-2-1-1 x-1

y-2=2x-1

y-2x=0

d2⊥d1 ⇒   2y+x=k , -1, -2 Lies on it ∴ k=-5

⇒2y+x+5=0

Now point of intersection  of d2 and L1
x-y+1=0  ......1

x+2y+5=0   .......2

on solving 1 & 2

-3y-4=0

y= -43

And point of intersection of d2 and L2

x+2y+5=0   ......3

14x-2y-10=0   ........4
On solving 3 & 4
And y= -83

15x-5=0

⇒ x=13

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About this question

This is a previous-year question from JEE Main 2016, 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.