Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 9

HARD

JEE Main/Advanced

IMPORTANT

Earn 100

If each of the vertices of a triangle has integral co-ordinates then the triangle may be:

50% studentsanswered this correctly

Important Questions on Coordinate Systems and Coordinates

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 10

The triangle

O A B

is right angled where points

O, A, B

are

(0, 0), (\cos θ, \sin θ)

and

(\cos ϕ, \sin ϕ)

respectively, then

θ

and

ϕ

are connected by the relation :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 11

A B C

is an isosceles triangle. If the co-ordinates of the base are

B (1, 3)

and

C (- 2, 7)

. The co-ordinates of vertex

A

can be:

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 12

If

A (a, a), B (- a, - a)

are two vertices of an equilateral triangle, then its third vertex is:

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 13

The medians

AD

and

B E

of the triangle with vertices

A (0, b), B (0, 0)

and

C (a, 0)

are mutually perpendicular if :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 14

The points

A (x, y), B (y, z)

and

C (z, x)

represents the vertices of a right angled triangle, if :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>Multiple Choice II>Q 15

Let the base of a triangle lie along the line

x = a

and be of length

2 a

. The area of this triangle is

a^{2}

, if the vertex lies on the line :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>FILL IN THE BLANKS>Q 1

The area enclosed by the lines

|x| + |y| = 1

is......

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 1 - Coordinate Systems and Coordinates>FILL IN THE BLANKS>Q 2

If

t_{1} + t_{2} + t_{3} = - t_{1} t_{2} t_{3}

, then the orthocentre of the triangle formed by the points

(a t_{1} t_{2}, a (t_{1} + t_{2})), (a t_{2} t_{3}, a (t_{2} + t_{3}))

and

(a t_{3} t_{1}, a (t_{3} + t_{1}))

lies on ...........