JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Straight Lines

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

\frac{k}{h}

equals:

(A) $- \frac{1}{7}$
(B) $\frac{1}{3}$ ✓ Correct
(C)3
(D)0

Answer: (B)

Solution

The three points

(h, k)

(1, 2)

and

(- 3, 4)

all lie on

L_{1}

, so find its slope from the two known points:

m_{1} = \frac{4 - 2}{- 3 - 1} = - \frac{1}{2}

, giving

L_{1} : x + 2 y = 5

. Since

L_{2}

is perpendicular, its slope is

2

, and through

(4, 3)

it is

L_{2} : 2 x - y = 5

. The point

(h, k)

lies on both, so solving

x + 2 y = 5

and

2 x - y = 5

together gives

y = 1

and

x = 3

. Hence

(h, k) = (3, 1)

and

\frac{k}{h} = \frac{1}{3}

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Straight Lines →

More JEE Main questions on Straight Lines

Let a point A lie between the parallel lines $L_{1}$ and $L_{2}$ such that its distances from $L_{1}$ and $L_{2}$ are 6 and 3 units, respectively. Then the area (in sq. units) of the equilateral triangle ABC , where the points B and C l …
JEE Main 2026View solution →
Among the statements
(S1): If $A (5, - 1)$ and $B (- 2, 3)$ are two vertices of a triangle, whose orthocentre is $(0, 0)$ , then its third vertex is $(- 4, - 7)$ and
(S2): If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., then the lines $a x + b y + c = 0$ are …
JEE Main 2026View solution →
A rectangle is formed by the lines $x = 0$ , $y = 0$ , $x = 3$ and $y = 4$ . Let the line L be perpendicular to $3 x + y + 6 = 0$ and divide the area of the rectangle into two equal parts. Then the distance of the point $(\frac{1}{2}, - 5)$ …
JEE Main 2026View solution →
Let $A (1, 2)$ and $C (- 3, - 6)$ be two diagonally opposite vertices of a rhombus, whose sides AD and BC are parallel to the line $7 x - y = 14$ . If $B (α, β)$ and $D (γ, δ)$ are the other two vertices, then …
JEE Main 2026View solution →
Let $A (1, 0), B (2, - 1)$ and $C (\frac{7}{3}, \frac{4}{3})$ be three points. If the equation of the bisector of the angle ABC is $α x + β y = 5$ , then the value of $α^{2} + β^{2}$ is
JEE Main 2026View solution →
Let the angles made with the positive x-axis by two straight lines drawn from the point $P (2, 3)$ and meeting the line $x + y = 6$ at a distance $\frac{2}{3}$ from the point P be $θ_{1}$ and $θ_{2}$ . Then the value of …
JEE Main 2026View solution →