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 points on y-axis,
    • which are at a distance of
    • 10
    • units
    • from the point
    • (
      (
      −
      5
      )
      ,
      (
      −
      6
      )
      )
    • (
      1
      ,
      (
      −
      7
      +
      5

      √

      3
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      6
      −
      5

      √

      3
      )
      )
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      +
      5

      √

      3
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      6
      −
      5

      √

      3
      )
      )
    • (
      2
      ,
      (
      −
      4
      +
      5

      √

      3
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      6
      −
      5

      √

      3
      )
      )
    • (
      0
      ,
      (
      −
      6
      +
      5

      √

      3
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      5
      −
      5

      √

      3
      )
      )
    • (
      0
      ,
      (
      −
      6
      +
      5

      √

      3
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      6
      −
      5

      √

      3
      )
      )
Question 2
2.
    • Find the centre of the circle passing through
    • the points
    • (
      8
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      (
      −
      6
      )
      ,
      (
      −
      1
      )
      )
    • and
    • (
      (
      −
      4
      )
      ,
      8
      )
  • (
    15
    8
    ,
    11
    4
    )
  • (
    23
    8
    ,
    7
    4
    )
  • (
    7
    8
    ,
    (
    −
    1
    4
    )
    )
  • (
    39
    8
    ,
    15
    4
    )
  • (
    31
    8
    ,
    3
    4
    )
Question 3
3.
    • The points
    • (
      (
      −
      7
      )
      ,
      (
      −
      7
      )
      )
    • ,
    • (
      7
      ,
      7
      )
    • and
    • (
      (
      −
      7
      2
      )
      ,
      (
      −
      7
      2
      )
      )
    • represents
  • isoceles triangle
  • right angle triangle
  • equilateral triangle
  • collinear points
Question 4
4.
    • The points
    • (
      4
      ,
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      2
      )
      )
    • and
    • (
      33
      7
      ,
      (
      −
      19
      7
      )
      )
    •  
    • represent
  • equilateral triangle
  • scalene triangle
  • collinear points
  • right angle triangle
  • isosceles triangle
Question 5
5.
    • Find the distance of the point
    • (
      (
      −
      8
      )
      ,
      1
      )
    • from origin
  • 4
    √

    65

  • √

    65

  • √

    68
  • 65

  • √

    62
Question 6
6.
    • The mid-point of the join of points
    • (
      5
      ,
      1
      )
    • and
    • (
      3
      ,
      4
      )
    • is
  • (
    6
    ,
    9
    2
    )
  • (
    4
    ,
    5
    2
    )
  • (
    2
    ,
    1
    2
    )
  • (
    5
    ,
    3
    2
    )
  • (
    3
    ,
    7
    2
    )
Question 7
7.
    • Find the centroid of the triangle formed by the points
    • (
      8
      ,
      6
      )
    • ,
    • (
      6
      ,
      (
      −
      2
      )
      )
    • and
    • (
      1
      ,
      5
      )
  • (
    6
    ,
    2
    )
  • (
    5
    ,
    3
    )
  • (
    4
    ,
    4
    )
  • (
    3
    ,
    1
    )
  • (
    7
    ,
    5
    )
Question 8
8.
    • A is a point on x-axis with abscissa
    • 7
    • and B is a point on y-axis
    • with ordinate
    • (-7)
    • .
    • Find the distance between A and B
  • 7

    √

    1
    2
  • 7
    4
    √

    2
  • 7

    √

    4
  • 7

    √

    2
  • 14
Question 9
9.
    • Find the coordinates of the mid points of the sides of the triangle formed by
    • (
      (
      −
      6
      )
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      (
      −
      4
      )
      ,
      3
      )
    • and
    • (
      (
      −
      5
      )
      ,
      3
      )
    • (
      (
      −
      5
      )
      ,
      (
      −
      1
      2
      )
      )
    • ,
    • (
      (
      −
      5
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      11
      2
      )
      ,
      (
      −
      1
      2
      )
      )
    • (
      (
      −
      6
      )
      ,
      1
      2
      )
    • ,
    • (
      (
      −
      9
      2
      )
      ,
      3
      )
    • ,
    • (
      (
      −
      11
      2
      )
      ,
      (
      −
      1
      2
      )
      )
    • (
      (
      −
      5
      )
      ,
      (
      −
      1
      2
      )
      )
    • ,
    • (
      (
      −
      9
      2
      )
      ,
      3
      )
    • ,
    • (
      (
      −
      15
      2
      )
      ,
      (
      −
      5
      2
      )
      )
    • (
      (
      −
      5
      )
      ,
      (
      −
      1
      2
      )
      )
    • ,
    • (
      (
      −
      9
      2
      )
      ,
      3
      )
    • ,
    • (
      (
      −
      9
      2
      )
      ,
      (
      −
      3
      2
      )
      )
    • (
      (
      −
      5
      )
      ,
      (
      −
      1
      2
      )
      )
    • ,
    • (
      (
      −
      9
      2
      )
      ,
      3
      )
    • ,
    • (
      (
      −
      11
      2
      )
      ,
      (
      −
      1
      2
      )
      )
Question 10
10.
    • 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
    )
  • (
    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
    )
  • (
    y

    1
    		  −  
    y

    2
    		  −  
    y

    3
    2
    ,
    x

    1
    		  −  
    x

    2
    		  −  
    x

    3
    2
    )