HARD

JEE Main

IMPORTANT

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If a $∆ A B C$ has vertices $A (- 1, 7), B (- 7, 1)$ and $C (5, - 5)$ , then its orthocentre has coordinates:

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Important Questions on Point and Straight Line

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 4 September 2020 Shift 1>Q 25

A triangle

A B C

lying in the first quadrant has two vertices as

A (1, 2)

and

B (3, 1)

. If

∠ B A C = 90^{o},

and

ar (Δ ABC) = 5 \sqrt{5}

sq. units, then the abscissa of the vertex

C

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 4 September 2020 Shift 2>Q 26

If the perpendicular bisector of the line segment joining the points

P (1, 4)

and

Q (k, 3)

has

y

-intercept equal to

- 4

, then a value of

k

is;

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 5 September 2020 Shift 1>Q 27

If the line,

2 x - y + 3 = 0

is at a distance

\frac{1}{\sqrt{5}}

and

\frac{2}{\sqrt{5}}

from the lines

4 x - 2 y + α = 0

and

6 x - 3 y + β = 0

respectively, then the sum of all possible values of

α

and

β

is ____________.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 6 September 2020 Shift 1>Q 28

A ray of light coming from the point $(2, 2 \sqrt{3})$ is incident at an angle $30 °$ on the line $x = 1$ at the point $A$ . The ray gets reflected on the line $x = 1$ and meets $x$ -axis at the point $B$ . Then, the line $A B$ passes through the point

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 6 September 2020 Shift 2>Q 29

Let

L

denote the line in the

x y

-plane with

x

and

y

intercepts as

3

and

1

respectively. Then the image of the point

(- 1, - 4)

in the line is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 7th January 2020 Shift 1>Q 30

Let

A (1, 0), B (6, 2)

and

C (\frac{3}{2}, 6)

be the vertices of a triangle

A B C .

P

is a point inside the triangle

A B C

such that the triangles

A P C, A P B

and

B P C

have equal areas, then the length of the line segment

P Q,

where

Q

is the point

(- \frac{7}{6}, - \frac{1}{3}),

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 7th January 2020 Shift 2>Q 31

The locus of the mid-points of the perpendiculars drawn from points on the line

x = 2 y

, to the line

x = y

, is.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Point and Straight Line>JEE Main - 8th January 2020 Shift 1>Q 32

The locus of a point which divides the line segment joining the point

(0, - 1)

and a point on the parabola

x^{2} = 4 y

internally in the ratio

1 : 2

, is:

If a ∆ABC has vertices A–1,7, B–7,1 and C5,–5, then its orthocentre has coordinates:

Important Questions on Point and Straight Line

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If a $∆ A B C$ has vertices $A (- 1, 7), B (- 7, 1)$ and $C (5, - 5)$ , then its orthocentre has coordinates: