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If the straight line $3 x + 4 y = 8$ is denoted by $L$ , then the points $(2, - 5), (- 5, 2)$

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Important Questions on Expressing Geometric Properties with Equations

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

If the family of straight lines

a x + b y + c = 0

, where

2 a + 3 b = 4 c

is concurrent at the point

P (l, m)

, then the foot of the perpendicular drawn from

P

to the line

x + y + 1 = 0

EASY

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

The length of the perpendicular from

(1, - 2)

to the line

12 x + 5 y + 63 = 0

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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:

EASY

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

Which one of the following points lies on the straight line

\frac{x - 1}{2} = \frac{y + 1}{4} = \frac{z - 2}{- 2}

EASY

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

The foot of the perpendicular drawn from the point

(1, 8, 4)

on the line joining the point

(0, - 11, 4)

and

(2, - 3, 1)

HARD

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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)

HARD

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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 :

EASY

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

The polar coordinate of a point

P

(2, - \frac{π}{4}) .

The polar coordinate of the point

Q

which is such that line joining

P Q

is bisected perpendicularly by the initial line, is

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

If the point

(a, a)

falls between the lines

|x + y| = 4,

then

HARD

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

C

is the reflection of

A (2, 4)

x

-axis and

B

is the reflection of

C

y

-axis then

|A B|

is -

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

The image of the point

(3, 5)

in the line

x - y + 1 = 0

, lies on :

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

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>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

The coordinates of the foot of the perpendicular from the point

(2, 3)

on the line

x + y - 11 = 0

MEDIUM

Mathematics>Geometry - II>Expressing Geometric Properties with Equations>Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems

A point on the straight line,

3 x + 5 y = 15

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

If the straight line 3x + 4y = 8 is denoted by L, then the points (2, -5), (-5, 2)

Important Questions on Expressing Geometric Properties with Equations

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If the straight line $3 x + 4 y = 8$ is denoted by $L$ , then the points $(2, - 5), (- 5, 2)$