Olympiad – Class X – Mathematics - Co-Ordinate Geometry

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Question - 1

A plane is divided into four equal parts by the coordinate axes.What is each part called?

  • A Quadrant
  • B Segment
  • C Sector
  • D Half-plane

Question - 2

In which quadrant(s) is abscissa positive?

  • A I only
  • B III only
  • C I and IV only
  • D II and III only

Question - 3

In which quadrant(s) is ordinate positive?

  • A II only
  • B I and II only
  • C I and IV only
  • D III and IV only

Question - 4

A point P is at a distance of 3 units from the Y-axis and 4 units from the X-axis. If P is in quadrant I,what are the co-ordinates of P?

  • A (-3, 4)
  • B (3, -4)
  • C (-3, -4)
  • D (3, 4)

Question - 5

What is the area of a triangle whose vertices are A(5, -1),B(3,8) and C(-4, 2)?

  • A 28 sq units
  • B 42.5 sq units
  • C 35 sq units
  • D 37.5 sq units

Question - 6

What is the distance between the points X(a, b) and Y(-a, -b)?

  • A \(\sqrt [ 2 ]{ { a }^{ 2 }+{ b }^{ 2 } } \)
  • B \(\sqrt { { a }^{ 2 }+{ b }^{ 2 } } \)
  • C 2a2+b2
  • D 2a2+2b2

Question - 7

What is the area of the rhombus formed by (3, 0), (4, 5), (-1, 4) and (-2, -1) as vertices?

  • A 16 sq. units
  • B 32 sq. units
  • C 42 sq. units
  • D 24 sq. units

Question - 8

What type of a triangle is formed with points (3, -3), (-3, 3) and \(\left( -3\sqrt { 3 } ,-3\sqrt { 3 } \right) \) as vertices?

  • A A scalene triangle
  • B An equilateral triangle
  • C An isosceles triangle
  • D A right triangle

Question - 9

For what value of 'x' are A(2,3), B(x, y) and C(4,3) the vertices of a right triangle with right angle at A?

  • A 2
  • B 4
  • C 5
  • D 3

Question - 10

What are the coordinates of the point X that divides the join of A(7, 4) and B(-3, 6) in the ratio 1 : 3?

  • A \(\left( \frac { 9 }{ 2 } ,\frac { 11 }{ 2 } \right) \)
  • B \(\left( \frac { 9 }{ 2 } ,\frac { 5 }{ 2 } \right) \)
  • C \(\left( \frac { 9 }{ 2 } ,\frac { 9 }{ 2 } \right) \)
  • D \(\left( \frac { 2 }{ 9 } ,\frac { 2 }{ 9 } \right) \)
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