Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 22

MEDIUM

JEE Main

IMPORTANT

Earn 100

Find the coordinates of the foot of the perpendicular drawn from the point $P (1, - 2)$ on the line $2 x - y + 1 = 0$ .

Important Questions on Straight Lines

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 22

Find the coordinates of the foot of perpendicular from the point

(- 1, 3)

to the line

3 x - 4 y - 16 = 0 .

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 23

Find the projection of the point

(1, 0)

on the line joining the points

(- 1, 2)

and

(5, 4)

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 24

Find the image of the point

(1, - 2)

with respect to the line mirror

2 x - y + 1 = 0

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 24

Assuming that straight lines work as the plane mirror for a point, find the image of the point

(1, 2)

in the line

x - 3 y + 4 = 0

.

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 24

Find the image of the point

(3, 8)

with respect to the line

x + 3 y = 7

assuming the line to be a plane mirror.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 25

If the image of the point

(2, 1)

with respect to the line mirror be

(5, 2)

, find the equation of the mirror.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 26

If

(h, r)

is the foot of the perpendicular from

(x_{1}, y_{1})

to

l x + m y + n = 0

, prove that

\frac{x_{1} - h}{l} = \frac{y_{1} - r}{m} = \frac{l x_{1} + m y_{1} + n}{l^{2} + m^{2}}

.

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 2 - Straight Lines>2.8>Q 27

Find the equation of the straight line passing through the point

(2, - 6)

and the point of intersection of the lines

5 x - 2 y + 14 = 0

and

2 y = 8 - 7 x

.