Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 38

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IMPORTANT

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Find the equations of the sides of a triangle having $(4, - 1)$ as a vertex, if the lines $x - 1 = 0$ and $x - y - 1 = 0$ are the equations of two internal bisectors of its angles.

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Important Questions on Point and Straight Line

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 39

A straight line

L

with negative slope passes through the point

(8, 2)

and cuts the positive coordinate axes at points

P

and

Q

, then the correct statement(s) among the following is/are (

0

is origin)

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 40

Equation of the diagonals of a rectangle are

y + 8 x - 17 = 0

and

y - 8 x + 7 = 0 .

If the area of the rectangle is

8

sq. units, then the equation of the sides of the rectangle is/are

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 41

Two adjacent sides of a rhombus are

2 x + 3 y = a - 5

and

3 x + 2 y = 4 - 2 a

and its diagonals intersect at the point

(1, 2),

then a can be

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 43

Let

D (x_{4}, y_{4})

be a point such that

A B C D

is a square and

M & P

are the midpoints of the sides

B C & C D

respectively, then

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 44

The equations of perpendicular of the sides

A B and A C

of triangle

A B C

are

x - y - 4 = 0

and

2 x - y - 5 = 0

respectively. If the vertex

A

is

(- 2, 3)

and circumcentre is

(\frac{3}{2}, \frac{5}{2}),

then which of the following is true.

HARD

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 45

Triangle

A B C

lies in the Cartesian plane and has an area of

70

square units. The coordinates of

B

and

C

are

(12, 19)

and

(23, 20)

respectively and the coordinates of

A

are

(p, q)

. The median to the side

B C

has slope

- 5,

then which can be corrected.

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Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 46

All the points lying on or inside the triangle formed by the points

(1, 3), (5, 6)

and

(- 1, 2)

satisfy

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 15 - Point and Straight Line>Exercise-2>Q 47

A \equiv (4, 2)

and

B \equiv (2, 4)

are two given points and a point

P

on the line

3 x + 2 y + 10 = 0

is given then which of the following is/are true.