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What is the measure of ∠EFC in the given figure?

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Important Questions on The Straight Line

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let

O

be the vertex and

Q

be any point on the parabola,

x^{2} = 8 y

. If the point

P

divides the line segment

O Q

internally in the ratio

1 : 3

, then the locus of

P

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

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>The Straight Line>Straight Line and a Point

If $Q (0, - 1, - 3)$ is the image of the point $P$ in the plane $3 x - y + 4 z = 2$ and $R$ is the point $(3, - 1, - 2)$ , then the area (in sq. units) of $Δ P Q R$ is

Question Image

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

A triangle

A B C

lying in the first quadrant has two vertices as

A (1, 2)

and

B (3, 1)

. If

∠ B A C = 90^{o},

and

ar (Δ ABC) = 5 \sqrt{5}

sq. units, then the abscissa of the vertex

C

is :

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

In a

∆ A B C

, medians,

A D

and

B E

are drawn. If

A D = 4

∠ D A B = \frac{π}{6} a n d ∠ A B E = \frac{π}{3}

, then the area of the

∆ A B C

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

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>The Straight Line>Straight Line and a Point

A triangle has a vertex at

(1, 2)

and the mid points of the two sides through it are

(- 1, 1)

and

(2, 3)

. Then the centroid of this triangle is:

HARD

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

A ray of light is projected from the origin at angle of

60 °

with the positive direction of

x

-axis towards the line,

y = 2,

which gets reflected from the point,

(α, 2) .

Then the distance of the reflected ray of light from the point

(2, 2)

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The area of the triangle formed by the points

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

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The coordinate of the point dividing internally the line joining the points

(4, - 2)

and

(8, 6)

in the ratio

7 : 5

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let

L

denote the line in the

x y

-plane with

x

and

y

intercepts as

3

and

1

respectively. Then the image of the point

(- 1, - 4)

in the line is :

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

If the points

(1, 1, λ) & (- 3, 0, 1)

, are equidistant from the plane,

3 x + 4 y - 12 z + 13 = 0,

then

λ

satisfies the equation:

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

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

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

The reflection of the point

(α, β, γ)

in the

x y -

plane is

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

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>The Straight Line>Straight Line and a Point

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 _____

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

O P Q R

is a square and

M, N

are the middle points of the sides

P Q

and

Q R

respectively, then the ratio of the areas of the square and

Δ O M N

EASY

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

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>The Straight Line>Straight Line and a Point

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.

MEDIUM

Mathematics>Coordinate Geometry>The Straight Line>Straight Line and a Point

Let

S

be the set of all triangles in the

x y

-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in

S

has area

50

sq. units, then the number of elements in the set

S

is:

What is the measure of ∠EFC in the given figure?

Important Questions on The Straight Line

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