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 point on x-axis which is equidistant
    • from the points
    • (
      1
      ,
      4
      )
    • and
    • (
      (
      −
      8
      )
      ,
      (
      −
      6
      )
      )
  • (
    (
    −
    47
    18
    )
    ,
    2
    )
  • (
    (
    −
    65
    18
    )
    ,
    (
    −
    1
    )
    )
  • (
    (
    −
    119
    18
    )
    ,
    (
    −
    2
    )
    )
  • (
    (
    −
    83
    18
    )
    ,
    0
    )
  • (
    (
    −
    101
    18
    )
    ,
    1
    )
Question 2
2.
    • Find the coordinates of the orthocentre of the triangle
    • whose vertices are
    • (
      0
      ,
      (
      −
      7
      )
      )
    • ,
    • (
      (
      −
      7
      )
      ,
      8
      )
    • and
    • (
      (
      −
      3
      )
      ,
      6
      )
  • (
    262
    23
    ,
    317
    23
    )
  • (
    216
    23
    ,
    271
    23
    )
  • (
    170
    23
    ,
    225
    23
    )
  • (
    239
    23
    ,
    248
    23
    )
  • (
    193
    23
    ,
    294
    23
    )
Question 3
3.
A point lies on negative side of y-axis at a distance of 6 units from x-axis. What are the coordinates of the point?
  • (
    (
    −
    6
    )
    ,
    0
    )
  • (
    6
    ,
    0
    )
  • (
    0
    ,
    6
    )
  • (
    0
    ,
    (
    −
    6
    )
    )
Question 4
4.
    • The points
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      3
      ,
      (
      −
      3
      )
      )
    • and
    • (
      6
      ,
      (
      −
      7
      )
      )
    • represent
  • isosceles right angled triangle
  • collinear points
  • scalene triangle
  • right angle triangle
  • equilateral triangle
Question 5
5.
    • If A
    • (
      5
      ,
      5
      )
    • and B
    • (
      (
      −
      1
      )
      ,
      (
      −
      3
      )
      )
    • are two points,
    • find the coordinates of the point C on AB produced so that AC = 2BC
  • (
    (
    −
    6
    )
    ,
    (
    −
    12
    )
    )
  • (
    (
    −
    8
    )
    ,
    (
    −
    10
    )
    )
  • (
    (
    −
    9
    )
    ,
    (
    −
    13
    )
    )
  • (
    (
    −
    7
    )
    ,
    (
    −
    11
    )
    )
  • (
    (
    −
    5
    )
    ,
    (
    −
    9
    )
    )
Question 6
6.
    • In what ratio is the join of
    • (
      (
      −
      9
      )
      ,
      2
      )
    • and
    • (
      5
      ,
      6
      )
    • divided by the line
    • (
      x
      +
      3
      		)
      =
      0
    • ?
  • 6
    		:
    6
  • 6
    		:
    8
  • 5
    		:
    8
  • 6
    		:
    11
  • 7
    		:
    8
Question 7
7.
    • Find the coordinates of the circumcentre of the triangle
    • whose vertices are
    • (
      6
      ,
      5
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      5
      )
      )
    • and
    • (
      3
      ,
      1
      )
  • (
    (
    −
    187
    2
    )
    ,
    80
    )
  • (
    (
    −
    189
    2
    )
    ,
    77
    )
  • (
    (
    −
    193
    2
    )
    ,
    79
    )
  • (
    (
    −
    195
    2
    )
    ,
    76
    )
  • (
    (
    −
    191
    2
    )
    ,
    78
    )
Question 8
8.
    • The points
    • (
      (
      −
      4
      )
      ,
      (
      −
      5
      )
      )
    • ,
    • (
      (
      −
      3
      )
      ,
      (
      −
      5
      )
      )
    • and
    • (
      (
      −
      7
      2
      )
      ,
      (
      −
      7
      2
      )
      )
    •  
    • represent
  • isosceles triangle
  • equilateral triangle
  • scalene triangle
  • right angle triangle
  • collinear points
Question 9
9.
    • In what ratio is the join of
    • (
      7
      ,
      (
      −
      4
      )
      )
    • and
    • (
      2
      ,
      8
      )
    • divided by the line
    • (
      −
      y
      		)
      =
      0
    • ?
  • 3
    		:
    8
  • 4
    		:
    8
  • 4
    		:
    10
  • 4
    		:
    6
  • 5
    		:
    8
Question 10
10.
    • The points
    • (
      5
      ,
      7
      )
    • ,
    • (
      (
      −
      7
      )
      ,
      (
      −
      7
      )
      )
    • and
    • (
      (
      −
      4
      )
      ,
      4
      )
    • represent
  • collinear points
  • scalene triangle
  • isosceles triangle
  • right angle triangle
  • equilateral triangle