MEDIUM

Earn 100

The sides $AB$ and $AC$ of the $∆ ABC$ have the equations $x + 2 = 0$ and $y - 3 = 0$ . The centroid of the triangle has the coordinates $(1, 1) .$ Find the equation of the median of the triangle passing through the vertex $A .$

Important Questions on Straight Lines

HARD

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

A straight line

L

at a distance of

4

units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of

60 °

with the line

x + y = 0 .

Then an equation of the line

L

is:
Note: In actual JEE Main paper, two options were correct for this question. Hence, we have changed one option.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

Two sides of a rhombus are along the lines,

x - y + 1 = 0

and

7 x - y - 5 = 0

. If its diagonals intersect at

(- 1, - 2)

, then which one of the following is a vertex of this rhombus ?

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

Suppose that the points

(h, k), (1, 2)

and

(- 3, 4)

lie on the line

L_{1} .

If a line

L_{2}

passing through the points

(h, k)

and

(4, 3)

is perpendicular to

L_{1},

then

\frac{k}{h}

equals:

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

Line joining the points

(0, 3)

and

(5, - 2)

is a tangent to the curve

y = \frac{a x}{1 + x}

, then

HARD

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

A square, of each side

2

, lies above the

x

-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle

30 °

with the positive direction of the

x

-axis , then the sum of the

x

-coordinates of the vertices of the square is

:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

If we reduce

3 x + 3 y + 7 = 0

to the form

x \cos α + y \sin α = p

, then the value of

p

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

A straight line through origin

O

meets the lines

3 y = 10 - 4 x

and

8 x + 6 y + 5 = 0

at points

A

and

B

respectively. Then,

O

divides the segment

A B

in the ratio

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

If a straight line passes through the point

(- 5, 4)

and makes an intercept of length

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

between the lines

x + 2 y + 1 = 0

and

x + 2 y - 1 = 0,

then the equation of that line is

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

Let

b, d > 0

. The locus of all points

P (r, θ)

for which the line

O P

(where

O

is the origin) cuts the line

r \sin θ = b

Q

such that

P Q = d

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

The equation of perpendicular bisectors of sides

A B

and

A C

of a

∆ A B C

are

x - y + 5 = 0

and

x + 2 y = 0

respectively. If the coordinates of vertex

A

are

(1, - 2),

then equation of

B C

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

The larger of two angles made with the

X

-axis of a straight line drawn through

(1, 2)

so that it intersects the line

x + y = 4

at a point distant

\sqrt{6} / 3

from the point

(1, 2)

HARD

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

Let

P S

be the median of the triangle with vertices

P (2, 2), Q (6, - 1)

and

R (7, 3)

. The equation of the line passing through

(1, - 1)

and parallel to

P S

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

The tangent to the curve

y = e^{2 x}

at the point

(0, 1)

meets the

x

-axis at

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

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;

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

x \cos θ + y \sin θ = p

is the normal form and

y = m x + c

is the slope - intercept form of the line

x + 2 y + 1 = 0,

then

\tan^{- 1} (\tan θ + m + c) =

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

The equation of the straight line in the normal form which is parallel to the lines

x + 2 y + 3 = 0

and

x + 2 y + 8 = 0

and dividing the distance between these two lines in the ratio

1 : 2

internally is

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

x \cos α + y \sin α = p

is the normal form of the equation of a straight line

x + \sqrt{3} y + 4 = 0

and

a, b

are respectively

X, Y -

intercepts of this line, then

\sqrt{3} π b p - 3 a α =

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

A line has slope

m

and

y

-intercept 4. The distance between the origin and the line is equal to

HARD

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

O (0, 0), A (1, 2), B (3, 4)

are the vertices of

∆ O A B .

The joint equation of the altitude and median drawn from

O

EASY

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the Equation of a Line

If a straight line passing through the point

P (- 3, 4)

is such that its intercepted portion between the coordinate axes is bisected at

P

, then its equation is :

The sides AB and AC of the ∆ABC have the equations x+2=0 and y–3=0. The centroid of the triangle has the coordinates (1, 1). Find the equation of the median of the triangle passing through the vertex A.

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

The sides $AB$ and $AC$ of the $∆ ABC$ have the equations $x + 2 = 0$ and $y - 3 = 0$ . The centroid of the triangle has the coordinates $(1, 1) .$ Find the equation of the median of the triangle passing through the vertex $A .$