ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Distance and Section Formulae
Question 1
1.
    • The line
    • (
      6
      x
      +
      20
      y
      +
      63
      		)
      =
      0
    • bisects which of the following pairs of points?
    • (
      1
      ,
      2
      )
    • ,
    • (
      (
      −
      3
      )
      ,
      (
      −
      7
      )
      )
    • (
      3
      ,
      4
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • (
      1
      ,
      2
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • (
      2
      ,
      1
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • (
      (
      −
      1
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
Question 2
2.
    • Find the coordinates of the points of trisection of the line segment
    • joining the points
    • (
      4
      ,
      2
      )
    • and
    • (
      4
      ,
      (
      −
      7
      )
      )
    • (
      5
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      4
      )
      )
    • (
      6
      ,
      1
      )
    • ,
    • (
      4
      ,
      (
      −
      4
      )
      )
    • (
      4
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      3
      ,
      (
      −
      3
      )
      )
    • (
      4
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      4
      )
      )
    • (
      2
      ,
      (
      −
      3
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      4
      )
      )
Question 3
3.
    • Find the points on x-axis,
    • which are at a distance of
    • 13
    • units
    • from the point
    • (
      (
      −
      7
      )
      ,
      4
      )
    • (
      (
      −
      7
      +
      3

      √

      17
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      7
      −
      3

      √

      17
      )
      ,
      0
      )
    • (
      (
      −
      5
      +
      3

      √

      17
      )
      ,
      2
      )
    • ,
    • (
      (
      −
      7
      −
      3

      √

      17
      )
      ,
      0
      )
    • (
      (
      −
      9
      +
      3

      √

      17
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      7
      −
      3

      √

      17
      )
      ,
      0
      )
    • (
      (
      −
      7
      +
      3

      √

      17
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      8
      −
      3

      √

      17
      )
      ,
      1
      )
    • (
      (
      −
      6
      +
      3

      √

      17
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      7
      −
      3

      √

      17
      )
      ,
      0
      )
Question 4
4.
    • Find the centre of the circle passing through
    • the points
    • (
      2
      ,
      7
      )
    • ,
    • (
      8
      ,
      (
      −
      7
      )
      )
    • and
    • (
      (
      −
      6
      )
      ,
      5
      )
  • (
    (
    −
    61
    31
    )
    ,
    (
    −
    128
    31
    )
    )
  • (
    1
    31
    ,
    (
    −
    66
    31
    )
    )
  • (
    (
    −
    30
    31
    )
    ,
    (
    −
    35
    31
    )
    )
  • (
    63
    31
    ,
    (
    −
    4
    31
    )
    )
  • (
    32
    31
    ,
    (
    −
    97
    31
    )
    )
Question 5
5.
    • Find the point on x-axis which is equidistant
    • from the points
    • (
      7
      ,
      5
      )
    • and
    • (
      3
      ,
      1
      )
  • (
    7
    ,
    1
    )
  • (
    9
    ,
    (
    −
    1
    )
    )
  • (
    10
    ,
    2
    )
  • (
    8
    ,
    0
    )
  • (
    6
    ,
    (
    −
    2
    )
    )
Question 6
6.
Distance of the given point from y-axis is
  • 3
  • 9
  • 6
  • 18
Question 7
7.
Distance of the given point from x-axis is
  • 0
  • 3
Question 8
8.
    • The points
    • (
      3
      ,
      3
      )
    • ,
    • (
      (
      −
      4
      )
      ,
      (
      −
      2
      )
      )
    • and
    • (
      (
      −
      4
      )
      ,
      5
      )
    • represent
  • right angle triangle
  • collinear points
  • isosceles triangle
  • scalene triangle
  • equilateral triangle
Question 9
9.
    • Find the radius of the circle passing through the points
    • (
      1
      ,
      8
      )
    • ,
    • (
      3
      ,
      5
      )
    • and
    • (
      7
      ,
      4
      )
  • 13
    10

    √

    20
  • 13
    10

    √

    17
  • 221
    10
  • 13
    10

    √

    15
  • 13
    10
    4
    √

    17
Question 10
10.
    • Two vertices of a triangle are
    • (
      (
      −
      8
      )
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      4
      ,
      1
      )
    • and its centriod is
    • (
      (
      −
      1
      )
      ,
      5
      3
      )
    • . Find the coordinates of the third vertex of the triangle
  • (
    (
    −
    1
    )
    ,
    (
    −
    8
    )
    )
  • (
    1
    ,
    (
    −
    8
    )
    )
  • (
    1
    ,
    8
    )
  • (
    (
    −
    1
    )
    ,
    8
    )
  • (
    8
    ,
    1
    )