Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 6

EASY

JEE Main

IMPORTANT

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Let $L$ be the line $2 x + y = 2$ . If the axes are rotated by $45 °$ , then the intercepts made by the line $L$ on the new axes are respectively

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Important Questions on Coordinates and Straight Lines

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 7

The sides of a triangle are the straight lines

x + y = 1, 7 y = x

and

\sqrt{3} y + x = 0

, then which of the following is an interior point of the triangle?

MEDIUM

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IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 8

A (1,3)

and

C (7,5)

are two opposite vertices of a square

A B C D .

The equation of a side through

A

is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 9

If

b x + c y = a,

where

a, b, c

are of the same sign, be a line such that the area enclosed by the line and the axes of reference is

\frac{1}{8}

square units, then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 10

If

6 a^{2} - 3 b^{2} - c^{2} + 7 a b - a c + 4 b c = 0

, then the family of lines

a x + b y + c = 0, | a | + | b | \neq 0

is concurrent at

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 11

One diagonal of a square is the portion of the line

\sqrt{3} x + y = 2 \sqrt{3}

intercepted by the axes. Then an extremity of the other diagonal is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 12

If the coordinates of the vertices of a triangle are rational numbers, then which of the following points of the triangle will always have rational coordinates?

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 5 - Coordinates and Straight Lines>5.1>Q 13

Line

L

is perpendicular to the line

5 x - y = 1

. The area of triangle formed by the line and coordinate axes is

5

. Its equation is

EASY

JEE Main

IMPORTANT

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

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