HARD

JEE Main

IMPORTANT

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A straight line $L$ with negative slope passes through the point $(800, 200)$ and cuts the positive coordinate axes at points $P$ and $Q$ . If $O$ is the origin, then the minimum value of $O P + O Q$ , as $L$ varies is...

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Important Questions on Coordinates and Straight Lines

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 1

The opposite angular points of a square are

(3, 4)

and

(1, - 1)

. Find the coordinates of the remaining vertices of the square.

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 2

A (- 4, 0)

and

B (- 1, 4)

are two given points.

C

and

D

are points which are symmetric to the given points

A

and

B

respectively with respect to

y

-axis. Calculate the perimeter of the trapezium

ABDC

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 3

Point

B

is symmetric to

A (4, - 1)

with respect to the bisector of the first quadrant. Find

AB

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 4

A line segment

A B

through the point

A (2, 0)

which makes an angle of

30 °

with the positive direction of

x

-axis is rotated about

A

in anticlockwise direction through an angle of

15 ° .

C

be the new position of point

B (2 + \sqrt{3}, 1),

find the coordinates of

C

EASY

JEE Main

IMPORTANT

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

The point

(1, - 2)

is reflected in the

x

-axis and then translated parallel to the positive direction of

x

-axis through a distance of

3

units. Find the coordinates of the point in the new position.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 6

The line segment joining

A (3, 0)

and

B (5, 2)

is rotated about

A

in the anticlockwise direction through an angle of

45 °

so that

B

goes to

C

. If

D

is the reflection of

C

y

-axis, find the coordinates of

D

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 7

A

(a_{1}, b_{1}), B (a_{2}, b_{2}), C (a_{3}, b_{3})

are the vertices of a

ΔABC .

The side

AB

is divided by the point

D

in the ratio

λ : μ

and then the line segment

DC

is divided by the point

E

in the ratio

u : λ + μ .

Find the coordinates of

E

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 8

The four points

A (α, 0), B (β, 0), C (γ, 0)

and

D (δ, 0)

are such that

α, β

are the roots of equation

a x^{2} + 2 h x + b = 0

and

γ, δ

are those of equation

a^{'} x^{2} + 2 h^{'} x + b^{'} = 0 .

Show that the sum of the ratios in which

C

and

D

divide

AB

is zero if

a b^{'} + a^{'} b = 2 h h^{'}

A straight line L with negative slope passes through the point 800,200 and cuts the positive coordinate axes at points P and Q. If O is the origin, then the minimum value of OP+OQ, as L varies is...

Important Questions on Coordinates and Straight Lines

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A straight line $L$ with negative slope passes through the point $(800, 200)$ and cuts the positive coordinate axes at points $P$ and $Q$ . If $O$ is the origin, then the minimum value of $O P + O Q$ , as $L$ varies is...