### Mathematics - Coordinate Geometry - I

#### Question - 1

The points (-a, -b), (0, 0), (a, b) and  (a2, ab) are

• A collinear
• B vertices of a parallelogram
• C vertices of a rectangle
• D None of these

#### Question - 2

If the three vertices of rectangle taken in order are the points (2, -2), (8, 4) and (5, 7) the coordinates of the fourth vertex are

• A (1, 1)
• B (1, -1)
• C (-1, 1)
• D None of these

#### Question - 3

If the vertices of a triangle have integral coordinates, then the triangle is

• A equilateral
• B never equilateral
• C always isosceles
• D None of these

#### Question - 4

The triangel with vertices at (2, 4), (2, 6) and ($2+\sqrt { 3 }$, 5) is

• A right angled
• B right angled and isosceles
• C equilateral
• D obtuse angled

#### Question - 5

The area of the triangle with vertices (a, b+c), (b, c+a) and (c, a+b) is

• A 0
• B abc
• C a+b+c
• D ab+bc+ca

#### Question - 6

The coordinates of the middle points of the sides of a triangle are (4, 2), (3, 3) and (2, 2); then the coordinates of its centroid me

• A $(3, \frac 7{3})$
• B (3,3)
• C (4, 3)
• D None of these

#### Question - 7

The area of the quadrilateral with vertices at F(2, -1), (4, 3), (-1, 2) and (-3, -2) is

• A 18
• B 36
• C 54
• D None of these

#### Question - 8

An equilateral triangle has one vertex at the point (3, 4) and another at the point (-2, 3). The co-ordinates of the third vertex are

• A (1,1) or (1, -1)
• B $(\frac { 1+\sqrt { 3 } }{ 2 } ,\frac { 7-5\sqrt { 3 } }{ 2 } )\quad or\quad (\frac { 1-\sqrt { 3 } }{ 2 } ,\frac { 7+5\sqrt { 3 } }{ 2 } )$
• C $(-\sqrt { 3 } ,\sqrt { 3 } )\quad or\quad (\sqrt { 3 } ,\sqrt { 3 } )$
• D None of these

#### Question - 9

The incentre fo the triangle whose vertices are (-36, 7), (20, 7) and (0, -8) is

• A (-1, 0)
• B (1, 0)
• C $(\frac 1{2}, 1)$
• D None of these

#### Question - 10

The orthocentre of the triangle whose vertices are A(0, 0), B(3, 4), C(4, 0) is

• A $(3, \frac {4}{5})$
• B $(3, \frac {5}{6})$
• C $(3, \frac {6}{7})$
• D $(3, \frac {3}{4})$