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
    • (
      (
      −
      9
      2
      )
      ,
      7
      2
      )
    • bisects A
    • (
      (
      −
      2
      )
      ,
      6
      )
    • and B
    • (
      x
      ,
      y
      )
    • , find
    • (
      x
      ,
      y
      )
  • (
    (
    −
    9
    )
    ,
    (
    −
    1
    )
    )
  • (
    (
    −
    5
    )
    ,
    3
    )
  • (
    (
    −
    6
    )
    ,
    0
    )
  • (
    (
    −
    7
    )
    ,
    1
    )
  • (
    (
    −
    8
    )
    ,
    2
    )
Question 2
2.
    • Find the coordinates of the orthocentre of the triangle
    • whose vertices are
    • (
      8
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      1
      ,
      1
      )
    • and
    • (
      3
      ,
      1
      )
  • (
    8
    ,
    37
    2
    )
  • (
    7
    ,
    39
    2
    )
  • (
    10
    ,
    41
    2
    )
  • (
    6
    ,
    33
    2
    )
  • (
    9
    ,
    35
    2
    )
Question 3
3.
    • The centroid of the triangle formed by the points
    • (
      x

      1
      ,
      y

      1
      )
    • ,
    • (
      x

      2
      ,
      y

      2
      )
    • and
    • (
      x

      3
      ,
      y

      3
      )
    • is
  • (
    x

    1
    		  −  
    x

    2
    		  −  
    x

    3
    3
    ,
    y

    1
    		  −  
    y

    2
    		  −  
    y

    3
    3
    )
  • (
    y

    1
    		  −  
    y

    2
    		  −  
    y

    3
    2
    ,
    x

    1
    		  −  
    x

    2
    		  −  
    x

    3
    2
    )
  • (
    x

    1
    		  +  
    x

    2
    		  +  
    x

    3
    3
    ,
    y

    1
    		  +  
    y

    2
    		  +  
    y

    3
    3
    )
  • (
    x

    1
    		  −  
    x

    2
    		  −  
    x

    3
    2
    ,
    y

    1
    		  −  
    y

    2
    		  −  
    y

    3
    2
    )
  • (
    y

    1
    		  +  
    y

    2
    		  +  
    y

    3
    2
    ,
    x

    1
    		  +  
    x

    2
    		  +  
    x

    3
    2
    )
Question 4
4.
    • The points
    • (
      4
      ,
      (
      −
      5
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      7
      )
      )
    • and
    • (
      (
      1
      +

      √

      3
      )
      ,
      (
      −
      6
      −
      3

      √

      3
      )
      )
    • represent
  • isosceles triangle
  • right angled triangle
  • equilateral triangle
  • scalene triangle
Question 5
5.
    • The points
    • (
      1
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      4
      )
    • and
    • (
      1
      2
      ,
      (
      −
      2
      )
      )
    • represents
  • right angle triangle
  • isoceles triangle
  • equilateral triangle
  • collinear points
Question 6
6.
    • The points
    • (
      (
      −
      6
      )
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      4
      )
      )
    • and
    • (
      0
      ,
      0
      )
    • represent
  • collinear points
  • equilateral triangle
  • isosceles right angled triangle
  • scalene triangle
  • right angle triangle
Question 7
7.
    • In what ratio is the join of
    • (
      (
      −
      2
      )
      ,
      6
      )
    • and
    • (
      9
      ,
      3
      )
    • divided by the line
    • (
      x
      −
      3
      		)
      =
      0
    • ?
  • 5
    		:
    8
  • 5
    		:
    3
  • 4
    		:
    6
  • 5
    		:
    6
  • 6
    		:
    6
Question 8
8.
    • Find the centre of the circle, the endpoints of whose
    • diameter are
    • (
      3
      ,
      5
      )
    • and
    • (
      3
      ,
      (
      −
      8
      )
      )
  • (
    (
    −
    3
    2
    )
    ,
    3
    )
  • (
    (
    −
    3
    )
    ,
    3
    2
    )
  • (
    (
    −
    3
    )
    ,
    (
    −
    3
    2
    )
    )
  • (
    3
    ,
    (
    −
    3
    2
    )
    )
  • (
    3
    ,
    3
    2
    )
Question 9
9.
    • If point P
    • (
      3
      ,
      5
      )
    • is equidistant from the points
    • (a,-2)
    • and
    • (
      (
      −
      6
      )
      ,
      7
      )
    • , find a
  • -1
  • -5
  • -4
  • -3
  • -2
Question 10
10.
    • Find the value of k such that the points
    • (
      (
      −
      4
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      5
      )
      ,
      21
      4
      )
    • and
    • (-8,k)
    • are collinear
  • 7
  • 3
  • 6
  • 8
  • 5