HARD

JEE Main

IMPORTANT

Earn 100

$A B$ is a side of a regular hexagon $A B C D E F$ and is of length $a$ with $A$ as the origin and $A B$ and $A E$ as the $x$ -axis and $y$ -axis respectively. Find the equation of lines $A C, A F$ and $B E$ .

Important Questions on Coordinates and Straight Lines

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 29

A straight road is at a distance of

5 \sqrt{2}

miles from a place. The shortest distance of the road from the place is in the

N . E .

direction. Do the following villages which is

6

miles East and

B E

miles North from the place, lie on the road or not ?

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 29

A straight road is at a distance of $5 \sqrt{2}$ miles from a place. The shortest distance of the road from the place is in the $N . E .$ direction. Do the following villages which is $4$ miles East and $3$ miles North from the place, lie on the road or not?

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 30

In the given figure, $P Q R$ is an equilateral triangle and $O S P T$ is a square. If $O T = 2$ units, find the equation of the sides $P T$ and $S P$ of the square.

Question Image

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 31

Two particles start from the same point

(2, - 1),

one moving

2

units along the line

x + y = 1

and the other

5

units along

x - 2 y = 4 .

If the particles move towards increasing

y

, find their new positions and the distance between them.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 32

One end of a thin elastic straight string is fixed at

A (4, - 1)

and the other end

B

is at

(1, 2)

in the unstretched condition. If the string is stretched to triple its length, find the coordinates of the other end in this stretched position.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 33

The line

A B

whose equation is

x - y = 2

cuts the

x

-axis at

A

and

B

(4, 2)

. The line

A B

is rotated about

A

through

45 °

in the anticlockwise direction. Find the new position of

B

and the equation of the line

A B

in the new position.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 34

Let

x - y

plane be vertical.

A

particle dropped gently from

(- 1, 1)

in the plane rebounds on the floor and returns to two-third of the height from which it has fallen. The equation of the line of intersection of

x - y

plane and the floor is

x + 2 y = 3

. Find the highest position of the particle after one rebound.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 35

The coordinates of the extremities of one diagonal of a square are

(1, 1)

and

(- 2, - 1)

. Find the coordinates of its other vertices and the equation of the other diagonal.

AB is a side of a regular hexagon ABCDEF and is of length a with A as the origin and AB and AE as the x-axis and y-axis respectively. Find the equation of lines AC,AF and BE.

Important Questions on Coordinates and Straight Lines

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$A B$ is a side of a regular hexagon $A B C D E F$ and is of length $a$ with $A$ as the origin and $A B$ and $A E$ as the $x$ -axis and $y$ -axis respectively. Find the equation of lines $A C, A F$ and $B E$ .