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The area of the triangle enclosed by the straight lines $x = 0, y = 0$ and $x + 2 y + 3 = 0$ in sq. unit is-

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Important Questions on Straight Lines

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

If the area of a triangle is

4

sq. units with vertices at

(- 2, 0), (0, 4)

and

(0, k)

, then the value of

k

EASY

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

The points

(0, \frac{8}{3}), (1, 3)

and

(82, 30)

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

EASY

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

The area of a triangle is

5

sq units. Two of its vertices are

(2, 1)

and

(3, - 2)

.

The third vertex lies on

y = x + 3

,

then the coordinates of the third vertex can be

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

:

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 :

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.

EASY

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

If the points

(2 a, a), (a, 2 a)

and

(a, a)

enclose a triangle of area

18

sq units, then the centroid of the triangle is equal to

MEDIUM

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

Two points

A

and

B

with co-ordinates

(1, 1)

and

(- 2, 3)

are given respectively. Then, the locus of a point

P

so that the area of

Δ P A B

is 9 sq.units is given by _____

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

In a circle with centre

O

, suppose

A, P, B

are three points on its circumference such that

P

is the mid-point of minor arc

A B

. Suppose when

∠ A O B = θ, \frac{a r e a (Δ A O B)}{a r e a (Δ A P B)} = \sqrt{5} + 2

∠ A O B

is doubled to

2 θ,

then the ratio

\frac{a r e a (Δ A O B)}{a r e a (Δ A P B)}

is.

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

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

MEDIUM

Mathematics>Coordinate Geometry>Straight Lines>Various Forms of the 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:

EASY

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

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of X-axis is

MEDIUM

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

Let

D

be the centroid of the triangle with vertices

(3, - 1)

(1, 3)

and

(2, 4)

. Let

P

be the point of intersection of the lines

x + 3 y - 1 = 10

and

3 x - y + 1 = 0

. Then, the line passing through the points

D

and

P

also passes through the point:

MEDIUM

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

Let the points of intersections of the lines

x - y + 1 = 0, x - 2 y + 3 = 0

and

2 x - 5 y + 11 = 0

are the mid points of the sides of a triangle

ABC .

Then the area of the triangle

ABC

EASY

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

The area of the triangle formed by the points

(a, b + c), (b, c + a), (c, a + b)

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:

The area of the triangle enclosed by the straight lines x=0, y=0 and x+2y+3=0 in sq. unit is-

Important Questions on Straight Lines

Learn and Prepare for any exam you want !

The area of the triangle enclosed by the straight lines $x = 0, y = 0$ and $x + 2 y + 3 = 0$ in sq. unit is-