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What is the slope of the line perpendicular to the line passing through the points $(- 5, 1)$ and $(- 2, 0)$ ?

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Important Questions on Straight Lines

HARD

Mathematics>Coordinate Geometry>Straight Lines>General 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>General Equation of a Line

The graph of the equation

x - 7 y = - 42

intersects the

y

-axis at

P (α, β)

and the graph of

6 x + y - 15 = 0

, intersects the

x

-axis at

Q (γ, δ)

. What is the value of

α + β + γ + δ

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

If the straight line

2 x - 3 y + 17 = 0

is perpendicular to the line passing through the points

(7, 17)

and

(15, β)

, then

β

equals :

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The tangent to the curve

y = x^{2} - 5 x + 5

, parallel to the line

2 y = 4 x + 1

, also passes through the point :

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Find the y-intercept of the line joining two points

(1, 3)

and

(3, 5)

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two vertices of a triangle are

(0, 2)

and

(4, 3) .

If its orthocenter is at the origin, then its third vertex lies in which quadrant?

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The equation of the line passing through the point

(- 3, 1)

and bisecting the angle between coordinate axes is

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

L

be the line passing through the point

P (1, 2)

such that its intercepted segment between the co-ordinate axes is bisected at

P

. If

L_{1}

is the line perpendicular to

L

and passing through the point

(- 2, 1)

, then the point of intersection of

L

and

L_{1}

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Answer the question on the basis of the following figure.

If AB is parallel to EC and $∠ B C D = 72^{°}$ , what will be that value of $∠ B A C$ ?

Question Image

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

S_{1}

and

S_{2}

are two straight lines such that the reflection of

S_{1}

S_{2}

and the reflection of

S_{2}

S_{1}

coincide, the angle between

S_{1}

and

S_{2}

is equal to?

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The number of values of $k$ , for which the system of equations :

$(k + 1) x + 8 y = 4 k$

$k x + (k + 3) y = 3 k - 1$

has no solution, is :

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The

y

-intercept of the line passing through

A (6, 1)

and perpendicular to the line

x - 2 y = 4

is …

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A ray of light along

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

gets reflected upon reaching

X -

axis, the equation of the reflected ray is

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Two sides of a parallelogram are along the lines,

x + y = 3

and

x - y + 3 = 0 .

If its diagonals intersect at

(2, 4),

then one of its vertex is:

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A straight line

L

through the point

(3, - 2)

is inclined at an angle of

60 °

to the line

\sqrt{3} x + y = 1 .

L

also intersects the

X

-axis, then the equation of

L

is:

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Distance between two parallel lines

y = 2 x + 4

and

y = 2 x - 1

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

Let

a, b, c

and

d

be non-zero numbers. If the point of intersection of the lines

4 a x + 2 a y + c = 0 & 5 b x + 2 b y + d = 0

lies in the fourth quadrant and is equidistant from the two axes then

HARD

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A ray of light passing through the point

(1, 2)

reflects on the

X

-axis at point

A

and the reflected ray passes through the point

(5, 3)

. The coordinate of

A

EASY

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

The two equations are

4 x + 4 k y - 6 = 0

and

x + 6 y - 12 = 0

. Find the value of

k

for which the pair of two linear equations represents the parallel lines.

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>General Equation of a Line

A rectangle is inscribed in a circle with a diameter lying along the line

3 y = x + 7 .

If the two adjacent vertices of the rectangle are

(- 8, 5)

and

(6, 5),

then the area of the rectangle

(

in sq. units

)

is:

What is the slope of the line perpendicular to the line passing through the points (-5,1) and (-2,0)?

Important Questions on Straight Lines

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What is the slope of the line perpendicular to the line passing through the points $(- 5, 1)$ and $(- 2, 0)$ ?