Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 77

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The points $A (1, 3)$ and $C (5, 1)$ are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient $2$ is

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Important Questions on Point and Straight Line

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 78

The point

(- 4, 5)

is the vertex of a square and one of its diagonals is

7 x - y + 8 = 0

. The equation of the other diagonal is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 79

Two straight lines

x + 2 y = 2

and

x + 2 y = 6

are given, then find the equation of the line parallel to given lines and divided distance between lines in the ratio

2 : 1

internally

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 80

The set of values of

' b'

for which the origin and the point

(1, 1)

lie on the same side of the straight line,

a^{2} x + a b y + 1 = 0 \forall a \in R, b > 0

are

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 81

The point

(a^{2}, a + 1)

is a point in the angle between the lines

3 x - y + 1 = 0

and

x + 2 y - 5 = 0

containing the origin, then

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 82

Find area of region represented by

3 x + 4 y > 12, 4 x + 3 y > 12

and

x + y < 4

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 83

The image of the point

A (1, 2)

by the line mirror

y = x

is the point

B

and the image of

B

by the line mirror

y = 0

is the point

(α, β),

then

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 84

The equation of perpendicular bisectors of the sides

A B

and

A C

of a triangle

A B C

are

x - y + 5 = 0

and

x + 2 y = 0

respectively. If the point

A

is

(1, - 2),

then the equation of the line

B C

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-1>Q 85

A light beam emanating from the point

A (3, 10)

reflects from the straight line

2 x + y - 6 = 0

and then passes through the point

B (4, 3) .

The equation of the reflected beam is

x + 3 y - λ = 0,

then the value of

λ

is