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 distance between the points
    • (
      6
      ,
      8
      )
    • and
    • (
      5
      ,
      8
      )
  • 1
  • 0
  • 2
  • (
    −
    2
    )
  • 4
Question 2
2.
    • Find the value of k such that the points
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      55
      13
      )
      ,
      51
      13
      )
    • and
    • (k,9)
    • are collinear
  • -3
  • -1
  • 0
  • -2
  • 2
Question 3
3.
    • If point P
    • (
      (
      −
      23
      14
      )
      ,
      6
      )
    • is equidistant from the points
    • (a,4)
    • and
    • (
      1
      ,
      2
      )
    • , find a
  • -5
  • -4
  • -8
  • -7
  • -6
Question 4
4.
    • The points
    • (
      (
      −
      3
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      1
      ,
      2
      )
    • and
    • (
      5
      ,
      (
      −
      2
      )
      )
    • represent
  • collinear points
  • scalene triangle
  • isosceles right angled triangle
  • equilateral triangle
  • right angle triangle
Question 5
5.
    • The points
    • (
      (
      −
      3
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      3
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      5
      ,
      3
      )
    • and
    • (
      (
      −
      1
      )
      ,
      3
      )
    • represent
  • rectangle
  • trapezium
  • parallelogram
  • rhombus
  • square
Question 6
6.
    • Find the ratio in which point
    • (
      35
      12
      ,
      37
      12
      )
    • divides the join of points
    • (
      7
      ,
      6
      )
    • and
    • (
      0
      ,
      1
      )
  • 8
    		:
    5
  • 7
    		:
    2
  • 7
    		:
    5
  • 7
    		:
    8
  • 6
    		:
    5
Question 7
7.
    • Find the coordinates of the mid points of the sides of the triangle formed by
    • (
      1
      ,
      5
      )
    • ,
    • (
      0
      ,
      1
      )
    • and
    • (
      8
      ,
      3
      )
    • (
      1
      2
      ,
      3
      )
    • ,
    • (
      4
      ,
      2
      )
    • ,
    • (
      5
      2
      ,
      2
      )
    • (
      1
      2
      ,
      3
      )
    • ,
    • (
      4
      ,
      2
      )
    • ,
    • (
      9
      2
      ,
      4
      )
    • (
      1
      2
      ,
      3
      )
    • ,
    • (
      6
      ,
      4
      )
    • ,
    • (
      9
      2
      ,
      4
      )
    • (
      1
      2
      ,
      3
      )
    • ,
    • (
      4
      ,
      2
      )
    • ,
    • (
      11
      2
      ,
      3
      )
    • (
      (
      −
      1
      2
      )
      ,
      4
      )
    • ,
    • (
      4
      ,
      2
      )
    • ,
    • (
      9
      2
      ,
      4
      )
Question 8
8.
    • In what ratio is the join of
    • (
      (
      −
      4
      )
      ,
      6
      )
    • and
    • (
      9
      ,
      1
      )
    • divided by the line
    • (
      x
      −
      4
      		)
      =
      0
    • ?
  • 8
    		:
    7
  • 9
    		:
    5
  • 8
    		:
    2
  • 8
    		:
    5
  • 7
    		:
    5
Question 9
9.
Distance of the given point from y-axis is
  • 5
  • 0
Question 10
10.
    • The points
    • (
      4
      ,
      5
      )
    • ,
    • (
      (
      −
      4
      )
      ,
      (
      −
      5
      )
      )
    • and
    • (
      28
      13
      ,
      35
      13
      )
    • represents
  • isoceles triangle
  • right angle triangle
  • equilateral triangle
  • collinear points