Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 14

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IMPORTANT

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If the equations of the hypotenuse and a side of a right-angled isosceles triangle be $x + m y = 1$ and $x = k$ respectively, then

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Important Questions on Coordinates and Straight Lines

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 15

The points on the line

x + y = 4

which lie at a unit distance from the line

4 x + 3 y = 10,

are

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 16

One side of a square of length

a

is inclined to the

x

-axis at an angle

α

with one of the vertices of the square at the origin. The equation of a diagonal of the square is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 17

Let the algebraic sum of the perpendicular distances from the points

A (2, 0), B (0, 2), C (1, 1)

to a variable line be zero. Then all such lines

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 18

The area of a triangle is

5

and two of its vertices are

A (2, 1)

and

B (3, - 2)

. The third vertex which lies on line

y = x + 3

is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 19

If

(α, β)

is the foot of perpendicular from

(x_{1}, y_{1})

to line

l x + m y + n = 0

, then

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 20

The integral values of

β

so that point

(0, β)

lies on or inside the triangle having sides

y + 3 x + 2 = 0, 3 y - 2 x - 5 = 0

and

4 y + x - 14 = 0

may be

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 21

The equation of two equal sides

A B

and

A C

of an isosceles triangle

A B C

are

x + y = 5

and

7 x - y = 3

respectively. If area of

∆ A B C

is

5

square units, then equation of

B C

may be

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 22

Two equal sides of an isosceles triangle are the lines

(a + b) x + (a - b) y - 2 a b = 0

and

(a - b) x + (a + b) y - 2 a b = 0

. If the third side passes through the point

(b - a, a - b)

, then the equation of third side may be