ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Distance and Section Formulae
Question 1
1.
    • If point P
    • (x,7)
    • is equidistant from the points
    • (
      0
      ,
      (
      −
      4
      )
      )
    • and
    • (
      2
      ,
      (
      −
      7
      )
      )
    • , find x
  • 77
    4
  • 79
    4
  • 39
    2
  • 81
    4
  • 41
    2
Question 2
2.
    • Find the lengths of the medians of a triangle whose vertices are
    • (
      8
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      5
      ,
      3
      )
    • and
    • (
      5
      ,
      7
      )
      • 2
      • ,
      		•
        1
        2

        √

        73
      • ,
      		•
        5
        2
      • 5
        2
      • ,
      		•
        2
      • ,
      		•
        2
      • 3

        √

        5
      • ,
      		•
        3
        2
      • ,
      		•
        3
        2

        √

        17
Question 3
3.
    • The points
    • (
      (
      −
      3
      )
      ,
      (
      −
      5
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      4
      )
      )
    • and
    • (
      1
      ,
      (
      −
      8
      )
      )
    •  
    • represent
  • parallelogram
  • rhombus
  • trapezium
  • rectangle
  • square
Question 4
4.
    • Find the relation between x and y such that the point P
    • (
      x
      ,
      y
      )
    • is equidistant from points
    • (
      0
      ,
      (
      −
      4
      )
      )
    • and
    • (
      8
      ,
      4
      )
  • (
    8
    x
    +
    10
    y
    −
    32
    		)
    =
    0
  • (
    4
    x
    −
    8
    y
    −
    32
    		)
    =
    0
  • (
    4
    x
    −
    11
    y
    −
    32
    		)
    =
    0
  • (
    8
    x
    +
    8
    y
    −
    32
    		)
    =
    0
  • (
    7
    x
    +
    8
    y
    −
    32
    		)
    =
    0
Question 5
5.
    • Find the value of k such that the points
    • (
      (
      −
      5
      )
      ,
      3
      )
    • ,
    • (
      (
      −
      5
      3
      )
      ,
      17
      3
      )
    • and
    • (k,7)
    • are collinear
  • 0
  • 3
  • -3
  • 1
  • -1
Question 6
6.
    • Determine the ratio in which the line
    • (
      2
      x
      −
      7
      y
      +
      17
      		)
      =
      0
    • divides the join of points
    • (
      1
      ,
      (
      −
      4
      )
      )
    • and
    • (
      (
      −
      1
      )
      ,
      4
      )
  • 47
    		:
    13
  • 47
    		:
    16
  • 48
    		:
    13
  • 46
    		:
    13
  • 47
    		:
    10
Question 7
7.
    • The points
    • (
      (
      −
      7
      )
      ,
      5
      )
    • ,
    • (
      7
      ,
      (
      −
      5
      )
      )
    • and
    • (
      (
      −
      35
      17
      )
      ,
      25
      17
      )
    • represents
  • collinear points
  • right angle triangle
  • equilateral triangle
  • isoceles triangle
Question 8
8.
    • If point P
    • (
      (
      −
      4
      )
      ,
      6
      )
    • bisects A
    • (
      (
      −
      5
      )
      ,
      4
      )
    • and B
    • (
      x
      ,
      y
      )
    • , find
    • (
      x
      ,
      y
      )
  • (
    (
    −
    1
    )
    ,
    10
    )
  • (
    (
    −
    4
    )
    ,
    9
    )
  • (
    (
    −
    2
    )
    ,
    7
    )
  • (
    (
    −
    3
    )
    ,
    8
    )
  • (
    (
    −
    5
    )
    ,
    6
    )
Question 9
9.
    • Find the area of the triangle
    • formed by the points
    • (
      7
      ,
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      )
    • and
    • (
      6
      ,
      5
      )
  • 9
  • 6
  • 4
  • 5
  • 7
Question 10
10.
    • The points
    • (
      (
      −
      5
      )
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      3
      ,
      (
      −
      4
      )
      )
    • and
    • (
      3
      ,
      1
      )
    • represent
  • equilateral triangle
  • collinear points
  • right angle triangle
  • scalene triangle
  • isosceles right angled triangle