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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2020 · 4 September · Evening Shift · Mathematics · Straight Lines

If the perpendicular bisector of the line segment joining the...

If the perpendicular bisector of the line segment joining the points P(1,4)P ( 1, 4 ) and Q(k,3)Q ( k, 3 ) has yy-intercept equal to −4- 4, then a value of kk is;

Options

  1. A−2- 2
  2. B−4- 4
  3. C14\sqrt{14}
  4. D15\sqrt{15}

Correct answer

B. −4- 4

Step-by-step solution

Mid point of PQPQ is \left(\dfrac{k + 1}{2}, \dfrac{7}{2}\right)<br/>Andslopeof<br />And slope ofPQ = \dfrac{1}{1 - k}<br/>Soequationofperpendicularbisectorof<br />So equation of perpendicular bisector ofPQ</p><p></p><p>y - \dfrac{7}{2} = ( k - 1 ) \left(x - \dfrac{k + 1}{2}\right)<br/>It′s<br />It'syinterceptintercept= - 4.So,thisequationmustsatisfy(0,−4). So, this equation must satisfy \left(0, - 4\right).

⇒−152=−(k2−12)⇒ - \dfrac{15}{2} = - \left(\dfrac{{k}^{2} - 1}{2}\right)
k2=16⇒k=±4{k}^{2} = 16 ⇒ k = \pm 4

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