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JEE Main 201912 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
12 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2019 · 12 January · Morning Shift · Mathematics · Straight Lines

If the straight line 2x - 3y + 17 = 0 is perpendicular to the line...

If the straight line 2x−3y+17=02x - 3y + 17 = 0 is perpendicular to the line passing through the points \left(7, 17\right) and \left(15, \beta\right), then β\beta equals :

Options

  1. A−5- 5
  2. B353\dfrac{35}{3}
  3. C55
  4. D−353- \dfrac{35}{3}

Correct answer

C. 55

Step-by-step solution

Slope of line 2x−3y+17=02x - 3y + 17 = 0 is 23\dfrac{2}{3}.

Slope of a line passing through \left(7, 17\right) and \left(15, \beta\right) is \dfrac{17 - \beta}{7 - 15}.

Since, both lines are perpendicular to each other, so product of slopes will be −1- 1.

⇒⇒\dfrac{17 - \beta}{7 - 15} \times \dfrac{2}{3} =−1- 1

⇒⇒\dfrac{17 - \beta}{- 8} =- \dfrac{3}{2}⇒17−β=12⇒β=5⇒ 17 - \beta = 12 ⇒ \beta = 5.

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