JEE Main 2021MathematicsStraight LinesEasyNumerical

JEE Main 2021 — Straight Lines Question with Solution

JEE Main 2021 (20 Jul Shift 2)

Question

Consider a triangle having vertices A(-2,3), B(1,9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC, bisects line BC, and intersects y-axis at point 0,α2, then the value of real number α is _______.

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Show full solutionCorrect answer: 9
Correct answer
9

Step-by-step explanation

We have,

AB=-2-12+3-92=45

AC=-2-32+3-82=50

BC=3-12+8-92=5

Here,

AC2=AB2+BC2

⇒(50)2=(45)2+(5)2

Hence, ∠B=90°, so circumcentre is the mid-point of hypotenuse i.e., AC.

Circumcenter ≡12,112

Mid-point of BC=2,172

Equation of line L is

y-112=112-17212-2x-12

⇒y=2x+92

Passing though 0,α2, so

α2=92⇒α=9

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About this question

This is a previous-year question from JEE Main 2021, 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.