Suppose that the points (h, k), (1, 2) and (- 3, 4) lie on the line L _ 1 . If a line L _ 2 passing through the points (h, k) and (4, 3) is perpendicular to L _ 1 , then (k)/(h) equals:

Correct answer: D. (1)/(3) Slope of line L _ 1 is (4 - 2)/(- 3 - 1) = (2)/(- 4) = (- 1)/(2) Hence slope of L _ 2 is 2 . From line L _ 1 , (k - 2)/(h - 1) = (- 1)/(2) ⇒ h + 2k = 5 …..(1) From line L _ 2 , (k - 3)/(h - 4) = 2 ⇒ k = 2h - 5 ..…(2) From (1) and (2) h = 3 and k = 1 ⇒ (k)/(h) = (1)/(3)

JEE Main 20198 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Straight Lines

JEE Main 2019 · 8 April · Evening Shift · Mathematics · Straight Lines

Suppose that the points (h, k), (1, 2) and (- 3, 4) lie on the line...

Suppose that the points

\left(h, k\right), \left(1, 2\right)

and \left(- 3, 4\right) lie on the line

{L}_{1} .

If a line

{L}_{2}passing through the

points \left(h, k\right) and \left(4, 3\right) is perpendicular to

{L}_{1},

then \dfrac{k}{h} equals: Suppose that the points (h, k), (1, 2) and (- 3, 4) lie on the line L _ 1 . If a line L _ 2 passing through the points

Options

A $- \dfrac{1}{7}$
B $3$
C $0$
D $\dfrac{1}{3}$

Correct answer

D. $\dfrac{1}{3}$

Step-by-step solution

Slope of line

{L}_{1}

\dfrac{4 - 2}{- 3 - 1} = \dfrac{2}{- 4} = \dfrac{- 1}{2}

Hence slope of

{L}_{2}

2 .

From line

{L}_{1}, \dfrac{k - 2}{h - 1} = \dfrac{- 1}{2}

⇒ h + 2k = 5

…..(1)
From line

{L}_{2}, \dfrac{k - 3}{h - 4} = 2

⇒ k = 2h - 5

..…(2)
From (1) and (2)

h = 3

and

k = 1

⇒ \dfrac{k}{h} = \dfrac{1}{3}

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