The image of the point $(-1,3,4)$ in the plane $x-2 y=0$ is

$\left(-\frac{17}{3},-\frac{19}{3}, 4\right)$

$\left(-\frac{17}{3},-\frac{19}{3}, 1\right)$

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JEE • MATHEMATICS • STRAIGHT LINES

Straight lines practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 8

Application +4 | -1

The incentre of a triangle with vertices (7, 1),

\left( { - 1,\;5} \right)

and

\left( {3 + 2\sqrt 3 ,\;3 + 4\sqrt 3 } \right)

View answer and explanation

Correct option: A

\left( {3 + \frac{2}{{\sqrt 3 }},3 + \frac{4}{{\sqrt 3 }}} \right)

Option A,

\left( {3 + \frac{2}{{\sqrt 3 }},3 + \frac{4}{{\sqrt 3 }}} \right)

, is correct because the triangle is equilateral, and the incenter coincides with the centroid, which can be calculated by averaging the coordinates.

2 Hard

2 of 8

Application +4 | -1

The lines

x\cos \alpha + y\sin \alpha = {p_1}

and

x\cos \beta + y\sin \beta = {p_2}

will be perpendicular, if

View answer and explanation

Correct option: C

\left| {\alpha - \beta } \right| = \frac{\pi }{2}

Option C (

\left| {\alpha - \beta } \right| = \frac{\pi }{2}

) is correct because the lines are perpendicular when the difference in their angles is

\frac{\pi }{2}

3 Hard

3 of 8

Application +4 | -1

The algebraic sum of the perpendicular distances from

A\left(x_1, y_1\right), B\left(x_2, y_2\right)

and

C\left(x_3, y_3\right)

to a variable line is zero, then the line passes through

View answer and explanation

Correct option: B

the centroid of

\triangle A B C

Option B is correct. If the algebraic sum of the perpendicular distances from

A(x_1, y_1)

B(x_2, y_2)

, and

C(x_3, y_3)

to a variable line is zero, then the line passes through the centroid of

\triangle ABC

4 Hard

4 of 8

Application +4 | -1

The image of the point

(-1,3,4)

in the plane

x-2 y=0

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the calculated image point does not match any of the provided options.

5 Hard

5 of 8

Analyzing +4 | -1

Let

m_1, m_2

be the slopes of two adjacent sides of a square of side a such that

a^2+11 a+3\left(m_1^2+m_2^2\right)

=220

. If one vertex of the square is

(10(\cos \alpha-

\sin \alpha), 10(\sin \alpha+\cos \alpha))

, where

\alpha \in\left(0, \frac{\pi}{2}\right)

and the equation of one diagonal is

(\cos \alpha-\sin \alpha) x

+(\sin \alpha+\cos \alpha) y=10

, then

72\left(\sin ^4 \alpha+\cos ^4 \alpha\right)

+a^2-3 a+13

is equal to :

View answer and explanation

Correct option: B

128

Option B (128) is the correct answer as it is obtained by calculating the side length and using the given equation to find the slopes, then substituting into the final expression.

6 Hard

6 of 8

Application +4 | -1

The area of a pentagon whose vertices are

\left( {4,1} \right),\left( {3,6} \right),\left( { - 5,1} \right),\left( { - 3, - 3} \right)

and

\left( { - 3,0} \right)

View answer and explanation

Correct option: A

30 sq. units

The correct answer is A (30 sq. units) because it is the absolute value of the sum of the areas of the triangles formed by the vertices of the pentagon.

7 Hard

7 of 8

Analyzing +4 | -1

The equation

{x^3} - 6{x^2}y + 11x{y^2} - 6{y^3} = 0

represents three straight lines passing through the origin, the slopes of which form an

View answer and explanation

Correct option: C

H.P.

Option C (H.P.) is correct because the slopes of the three lines form a Harmonic Progression.

8 Hard

8 of 8

Analyzing +4 | -1

The line

L

has intercepts

a

and

b

on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If

p

and

q

are the intercepts of the line

L

on the new axes, then

\frac{1}{a^2}-\frac{1}{p^2}+\frac{1}{b^2}-\frac{1}{q^2}

is equal to

View answer and explanation

Correct option: B

Option B (0) is correct because the perpendicular distance from the origin to the line remains invariant under rotation of axes.

Revision notes and key takeaways

Review STRAIGHT LINES in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 8 single-correct-answer MCQs on STRAIGHT LINES.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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