Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 25

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If the vertices $P, Q, R$ of a triangle $PQR$ are rational points, which of the following points of the triangle $PQR$ is/are always rational point(s)?

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Important Questions on Point and Straight Line

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 26

Let

P Q R

be a right angled isosceles triangle, right angled at

P (2, 1)

. If the equation of the line

Q R

is

2 x + y = 3

, then the equation representing the pair of lines

P Q

and

P R

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 27

Coordinates of a point which is at

3

units distance from the point

(1, - 3)

on the line

2 x + 3 y + 7 = 0

is/are-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 28

The angle between the lines

y - x + 5 = 0

and

\sqrt{3} x - y + 7 = 0

is/are-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 29

If line

y - x + 2 = 0

is shifted parallel to itself towards the

x

-axis by a perpendicular distance of

3 \sqrt{2}

units, then the equation of the new line is may be-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 30

Three lines

p x + q y + r = 0, q x + r y + p = 0

and

r x + p y + q = 0

are concurrent, if

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 31

All points lying inside the triangle formed by the points

(1, 3), (5, 0)

and

(- 1, 2)

satisfy

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-2>Q 32

The diagonals of a square are along the pair of lines whose equation is

2 x^{2} - 3 x y - 2 y^{2} = 0

. If

(2, 1)

is a vertex of the square, then the vertex of the square adjacent to it may be-

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Beta Question Bank for Engineering: Mathematics>Chapter 16 - Point and Straight Line>EXERCISE-3>Q 10

If the point

P (3, 5)

divides the line joining

A (1, 3)

&

B (7, 9)

and harmonic conjugate of

P

w.r.t.

A

&

B

is

Q (a, b)

, then

a + b

is