ICSE Board Practice

Class VI Class VII Class VIII Class IX Class X
ICSE Grade X - Equation of a Straight Line
Question 1
1.
    • The equation of the line passing through the points
    • (
      x

      1
      ,
      y

      1
      )
    • and
    • (
      x

      2
      ,
      y

      2
      )
    • is
a)
    • (
      y
      		  −  
      y

      1
      ) =
      y

      2
      		  +  
      y

      1
      x

      2
      		  +  
      x

      1
      (
      x
      		  −  
      x

      1
      )
b)
    • (
      x
      		  −  
      x

      1
      ) =
      x

      2
      		  −  
      x

      1
      y

      2
      		  −  
      y

      1
      (
      y
      		  −  
      y

      1
      )
c)
    • (
      y
      		  −  
      y

      1
      ) =
      y

      2
      		  −  
      y

      1
      x

      2
      		  −  
      x

      1
      (
      x
      		  −  
      x

      1
      )
d)
    • (
      x
      		  −  
      x

      1
      ) =
      x

      2
      		  +  
      x

      1
      y

      2
      		  +  
      y

      1
      (
      y
      		  −  
      y

      1
      )
  • {b,c}
  • {a,b}
  • {d,c}
  • {a,c,b}
  • {a,d,b}
Question 2
2.
    • Find the equation of the line passing through the points
    • (
      1
      ,
      0
      )
    • and
    • (
      (
      −
      6
      )
      ,
      (
      −
      6
      )
      )
  • (
    −
    6
    x
    +
    7
    y
    +
    12
    		)
    =
    0
  • (
    −
    6
    x
    +
    7
    y
    −
    1
    		)
    =
    0
  • (
    −
    5
    x
    +
    7
    y
    +
    6
    		)
    =
    0
  • (
    −
    7
    x
    +
    7
    y
    +
    6
    		)
    =
    0
  • (
    −
    6
    x
    +
    7
    y
    +
    6
    		)
    =
    0
Question 3
3.
    • Find the point of intersection of
    • (
      6
      x
      −
      42
      		)
      =
      0
    • and
    • the line joining points
    • (
      4
      ,
      6
      )
    • and
    • (
      (
      −
      4
      )
      ,
      2
      )
  • (
    5
    ,
    11
    2
    )
  • (
    6
    ,
    17
    2
    )
  • (
    7
    ,
    15
    2
    )
  • (
    9
    ,
    19
    2
    )
  • (
    8
    ,
    13
    2
    )
Question 4
4.
    • Which of the following pairs of lines are perpendicular?
      • (
        2
        x
        −
        13
        y
        +
        62
        		)
        =
        0
      • ,
      • (
        11
        x
        +
        2
        y
        +
        21
        		)
        =
        0
      • (
        2
        x
        −
        13
        y
        +
        62
        		)
        =
        0
      • ,
      • (
        13
        x
        +
        2
        y
        +
        23
        		)
        =
        0
      • (
        2
        x
        −
        13
        y
        +
        62
        		)
        =
        0
      • ,
      • (
        −
        2
        x
        +
        13
        y
        +
        97
        		)
        =
        0
      • (
        2
        x
        −
        13
        y
        +
        62
        		)
        =
        0
      • ,
      • (
        −
        15
        x
        +
        13
        y
        +
        136
        		)
        =
        0
Question 5
5.
    • Find the relation between x and y if the points
    • (
      x
      ,
      y
      )
    • ,
    • (
      3
      ,
      4
      )
    • and
    • (
      4
      ,
      (
      −
      8
      )
      )
    • are collinear
  • (
    −
    3
    x
    +
    4
    y
    −
    7
    		)
    =
    0
  • (
    −
    9
    x
    +
    5
    y
    −
    14
    		)
    =
    0
  • (
    10
    y
    +
    80
    		)
    =
    0
  • (
    9
    x
    +
    5
    y
    +
    4
    		)
    =
    0
  • (
    −
    12
    x
    −
    y
    +
    40
    		)
    =
    0
Question 6
6.
Two straight lines are perpendicular if and only if the product of their slopes is
  • 1
  • undefined
  • 90
  • 0
  • -1
Question 7
7.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        9
        )
        ,
        (
        −
        2
        )
        )
      • ,
      • (
        (
        −
        9
        )
        ,
        (
        −
        1
        )
        )
      • ,
      • (
        (
        −
        9
        )
        ,
        0
        )
      • ,
      • (
        (
        −
        9
        )
        ,
        1
        )
      • ,
      • (
        (
        −
        9
        )
        ,
        2
        )
    • ?
  • x
    =
    (
    −
    9
    		)
  • (
    9
    x
    +
    8
    y
    −
    6
    		)
    =
    0
  • y
    =
    (
    −
    16
    13
    x
    −
    144
    13
    		)
  • (
    −
    16
    x
    −
    13
    y
    −
    21
    		)
    =
    0
  • x
    =
    (
    16
    13
    y
    −
    9
    		)
Question 8
8.
The equation of the x-axis is
a)
    • x
      =
      1
b)
    • y
      =
      0
c)
    • x
      =
      0
d)
    • y
      =
      1
e)
    • x
      =
      y
  • {a,b}
  • {d,e,b}
  • {c,b}
  • {b}
Question 9
9.
    • Find the x-intercept of the line passing
    • through points
    • (
      (
      −
      5
      )
      ,
      (
      −
      3
      )
      )
    • and
    • (
      (
      −
      4
      )
      ,
      1
      )
  • (
    -9
    2
    		 )
  • (
    -19
    4
    		 )
  • 17
  • (
    -15
    4
    		 )
  • (
    -4
    1
    4
    		 )
Question 10
10.
    • Find the point of intersection of x-axis and
    • the line joining points
    • (
      7
      ,
      5
      )
    • and
    • (
      0
      ,
      6
      )
  • (
    6
    ,
    0
    )
  • (
    (
    −
    42
    )
    ,
    0
    )
  • (
    0
    ,
    (
    −
    6
    )
    )
  • (
    42
    ,
    0
    )