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 \((3, \frac {3}{4})\)
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