ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Distance and Section Formulae
Question 1
1.
    • Find the lengths of the medians of a triangle whose vertices are
    • (
      (
      −
      1
      )
      ,
      (
      −
      7
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • and
    • (
      (
      −
      8
      )
      ,
      (
      −
      6
      )
      )
      • 7
        2
      • ,
      		•
        5
        2

        √

        2
      • ,
      		•
        1
        2
      • 1
        2

        √

        53
      • ,
      		•
        5
        2

        √

        2
      • ,
      		•
        1
        2

        √

        197
      • 1
        2
      • ,
      		•
        7
        2
      • ,
      		•
        7
        2
Question 2
2.
    • The points
    • (
      (
      −
      5
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      3
      )
      ,
      2
      )
    • and
    • (
      (
      −
      1
      )
      ,
      3
      )
    • represent
  • equilateral triangle
  • scalene triangle
  • right angle triangle
  • collinear points
  • isosceles triangle
Question 3
3.
    • Find the value of k such that the points
    • (
      (
      −
      4
      )
      ,
      0
      )
    • ,
    • (
      1
      5
      ,
      21
      5
      )
    • and
    • (3,k)
    • are collinear
  • 8
  • 10
  • 7
  • 6
  • 5
Question 4
4.
    • A is a point on x-axis with abscissa
    • (-3)
    • and B is a point on y-axis
    • with ordinate
    • (-4)
    • .
    • Find the distance between A and B
  • 6
  • 5
  • 2
  • 7
  • 4
Question 5
5.
    • Find the point that bisects
    • (
      (
      −
      6
      )
      ,
      4
      )
    • and
    • (
      3
      ,
      (
      −
      6
      )
      )
  • (
    (
    −
    3
    2
    )
    ,
    (
    −
    1
    )
    )
  • (
    (
    −
    7
    2
    )
    ,
    (
    −
    3
    )
    )
  • (
    1
    2
    ,
    1
    )
  • (
    (
    −
    1
    2
    )
    ,
    (
    −
    2
    )
    )
  • (
    (
    −
    5
    2
    )
    ,
    0
    )
Question 6
6.
    • Two vertices of a triangle are
    • (
      (
      −
      2
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      4
      )
      ,
      1
      )
    • and its centriod is
    • (
      (
      −
      4
      3
      )
      ,
      8
      3
      )
    • . Find the coordinates of the third vertex of the triangle
  • (
    (
    −
    2
    )
    ,
    (
    −
    8
    )
    )
  • (
    8
    ,
    2
    )
  • (
    2
    ,
    (
    −
    8
    )
    )
  • (
    (
    −
    2
    )
    ,
    8
    )
  • (
    2
    ,
    8
    )
Question 7
7.
    • Find the distance of the point
    • (
      5
      ,
      (
      −
      8
      )
      )
    • from origin
  • 89

  • √

    92

  • √

    89
  • 4
    √

    89

  • √

    87
Question 8
8.
    • One end of the diameter of a circle is
    • (
      (
      −
      3
      )
      ,
      0
      )
    • .
    • If the centre is
    • (
      (
      −
      1
      2
      )
      ,
      1
      2
      )
    • ,
    • find the other end of the diameter
  • (
    3
    ,
    0
    )
  • (
    2
    ,
    1
    )
  • (
    4
    ,
    3
    )
  • (
    0
    ,
    (
    −
    1
    )
    )
  • (
    1
    ,
    2
    )
Question 9
9.
    • Find the area of the quadrilateral formed by
    • (
      (
      −
      3
      )
      ,
      (
      −
      7
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      2
      )
      )
    • and
    • (
      (
      −
      4
      )
      ,
      (
      −
      4
      )
      )
  • 16
  • 14
  • 18
  • 13
  • 15
Question 10
10.
    • The points
    • (
      (
      −
      4
      )
      ,
      1
      )
    • ,
    • (
      7
      ,
      7
      )
    • and
    • (
      (
      3
      2
      −
      3

      √

      3
      )
      ,
      (
      4
      +
      11
      2

      √

      3
      )
      )
    • represent
  • isosceles triangle
  • scalene triangle
  • right angled triangle
  • equilateral triangle