Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 93

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If an equilateral triangle, having centroid at the origin, has a side along the line, $x + y = 2,$ then the area (in sq units) of this triangle is

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Important Questions on Straight Line

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 94

Consider a

∆ A B C

with vertices at

(0, - 3) (- 2 \sqrt{3}, 3)

and

(2 \sqrt{3}, 3)

, respectively. The incentre of the triangle with vertices at the mid-points of the sides of

Δ A B C

is

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 95

If

(3, - 4)

and

(- 6, 5)

are the extremities of a diagonal of a parallelogram and

(2, 1)

is the third vertex, then its fourth vertex is-

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 96

A line passing through the point

P (1, 2)

meets the line

x + y = 7

at a distance of

3

units from

P

. Then, the slope of this line satisfies the equation

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 97

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

is

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 98

In a triangle

P Q R,

the co-ordinates of the points

P

and

Q

are

(- 2, 4)

and

(4, - 2)

respectively. If the equation of the perpendicular bisector of

P R

is

2 x - y + 2 = 0,

then the centre of the circumcircle of the

Δ P Q R

is:

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 99

The equation of a straight line, which passes through the point

(- 3, 5)

such that the portion of it between the axes is divided by the point in the ratio

5 : 3

internally (reckoning from

x

-axis), will be-

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 100

On the portion of the straight line

x + 2 y = 4

intercepted between the axes, a square is constructed on the side of the line away from the origin. Then the point of intersection of its diagonals has co-ordinates:

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Mathematics Crash Course MHT-CET>Chapter 5 - Straight Line>Exercise 1>Q 101

If the point

(p, 5)

lies on the line parallel to the

Y

-axis and passing through the intersection of the lines

2 (a^{2} + 1) x + b y + 4 (a^{3} + a) = 0

and

(a^{2} + 1) x - 3 b y + 2 (a^{3} + a) = 0

, then

p

is equal to