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If an equilateral triangle, having centroid at the origin, has a side along the line $x + y = 2,$ then the area (in sq.units) of this triangle is

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Important Questions on Straight Lines

HARD

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

For $a > b > c > 0$ , the distance between $(1, 1)$ and the point of intersection of the lines $a x + b y + c = 0$ and $b x + a y + c = 0$ is less than $2 \sqrt{2}$ . Then

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

Let

a \neq 0, b \neq 0, c

be three real numbers and

L (p, q) = \frac{a p + b q + c}{\sqrt{a^{2} + b^{2}}}, \forall p, q \in R

. If

L (\frac{2}{3}, \frac{1}{3}) + L (\frac{1}{3}, \frac{2}{3}) + L (2, 2) = 0

, then the line

a x + b y + c = 0

always passes through the fixed point

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From 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:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

A point on the straight line,

3 x + 5 y = 15

which is equidistant from the coordinate axes will lie only in:

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

Slope of a line passing through

P (2, 3)

and intersecting the line

x + y = 7

at a distance of

4

units from

P,

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

If the two lines

x + (a - 1) y = 1

and

2 x + a^{2} y = 1, (a \in R - \{0,1\})

are perpendicular, then the distance of their point of intersection from the origin is

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

Let

S

be a subset of the plane defined by

S = \{(x, y) : | x | + 2 | y | = 1\}

. Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with

S

EASY

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

An equation of a straight line passing through the intersection of the straight lines

3 x - 4 y + 1 = 0

and

5 x + y - 1 = 0

and making non-zero, equal intercepts on the axes is

HARD

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

If the line,

2 x - y + 3 = 0

is at a distance

\frac{1}{\sqrt{5}}

and

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

from the lines

4 x - 2 y + α = 0

and

6 x - 3 y + β = 0

respectively, then the sum of all possible values of

α

and

β

is ____________.

EASY

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

The length of perpendicular from the point

(a \cos α, a \sin α)

upon the straight line

y = x \tan α + c, c > 0

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

A ray of light coming from the point $(2, 2 \sqrt{3})$ is incident at an angle $30 °$ on the line $x = 1$ at the point $A$ . The ray gets reflected on the line $x = 1$ and meets $x$ -axis at the point $B$ . Then, the line $A B$ passes through the point

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From 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 :

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

If the point

(a, a)

falls between the lines

|x + y| = 4,

then

HARD

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

Given three points

P, Q, R

with

P (5, 3)

and

R

lies on the

x -

axis. If the equation of

R Q

x - 2 y = 2

and

P Q

is parallel to the

x -

axis, then the centroid of

Δ P Q R

lies on the line

HARD

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

A

ray of light passing through the point

(1, 2)

is reflected on the

x

-axis at a point

P

and passes through the point

(5, 3)

then the abscissa of a point

P

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

The set of all possible values of

θ

in the interval

(0, π)

for which the points

(1, 2)

and

(\sin θ, \cos θ)

lie on the same side of the line

x + y = 1

is?

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

The length of the perpendicular from

(1, - 2)

to the line

12 x + 5 y + 63 = 0

HARD

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

If a line

L

is perpendicular to the line

5 x - y = 1,

and the area of the triangle formed by the line

L

and the coordinate axes is

5

sq units, then the distance of the line

L

from the line

x + 5 y = 0

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From 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

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Distance of a Point From a Line

Find the distance of the point

(- 1, 1)

from the line

12 (x + 6) = 5 (y - 2) .

If an equilateral triangle, having centroid at the origin, has a side along the line x+y=2, then the area (in sq.units) of this triangle is

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

If an equilateral triangle, having centroid at the origin, has a side along the line $x + y = 2,$ then the area (in sq.units) of this triangle is