06 - Let's Recap - Coordinate Geometry - Class 10 - Maths Class 10 Notes | EduRev

Crash Course for Class 10 Maths by Let's tute

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Class 10 : 06 - Let's Recap - Coordinate Geometry - Class 10 - Maths Class 10 Notes | EduRev

 Page 1


 
(Coordinate geometry is used to locate the position of a point on a plane with the 
help of a pair of coordinate axes) 
 
1. Coordinate Axes: Let      and      be two perpendicular lines 
intersecting at O. The point O is called the origin and      (x-axis) 
and      (y-axis) are called coordinate axes. 
 
 
 
2. The distance of a point from the x-axis is called its y-coordinate, or 
ordinate. 
  
3. The distance of a point from the y-axis is called its x-coordinate, or 
abscissa.  
 
 
 
4. Distance formula: 
 
a. Distance between two points [suppose, A( 
 
  
 
) and B( 
 
  
 
)] on a 
plane 
Page 2


 
(Coordinate geometry is used to locate the position of a point on a plane with the 
help of a pair of coordinate axes) 
 
1. Coordinate Axes: Let      and      be two perpendicular lines 
intersecting at O. The point O is called the origin and      (x-axis) 
and      (y-axis) are called coordinate axes. 
 
 
 
2. The distance of a point from the x-axis is called its y-coordinate, or 
ordinate. 
  
3. The distance of a point from the y-axis is called its x-coordinate, or 
abscissa.  
 
 
 
4. Distance formula: 
 
a. Distance between two points [suppose, A( 
 
  
 
) and B( 
 
  
 
)] on a 
plane 
 
 
 
 
 
 
 
  
 
    
 
   
 
 
 
                                  ( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
                              v( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
Note: Since distance is always non-negative, we take only the positive value of the             
square root. 
 
 
b. Distance of a point A(   ) from the origin O(   ) on a plane. 
 
              v 
 
  
 
 
Page 3


 
(Coordinate geometry is used to locate the position of a point on a plane with the 
help of a pair of coordinate axes) 
 
1. Coordinate Axes: Let      and      be two perpendicular lines 
intersecting at O. The point O is called the origin and      (x-axis) 
and      (y-axis) are called coordinate axes. 
 
 
 
2. The distance of a point from the x-axis is called its y-coordinate, or 
ordinate. 
  
3. The distance of a point from the y-axis is called its x-coordinate, or 
abscissa.  
 
 
 
4. Distance formula: 
 
a. Distance between two points [suppose, A( 
 
  
 
) and B( 
 
  
 
)] on a 
plane 
 
 
 
 
 
 
 
  
 
    
 
   
 
 
 
                                  ( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
                              v( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
Note: Since distance is always non-negative, we take only the positive value of the             
square root. 
 
 
b. Distance of a point A(   ) from the origin O(   ) on a plane. 
 
              v 
 
  
 
 
 
 
 
5. Section formula: 
a. The coordinates of the point A(   ) which divides the line segment 
PQ [where, P( 
 
  
 
) and Q( 
 
  
 
)], internally, in the ratio  
 
 
   
 
 are 
 
 
 
(
 
 
 
 
  
 
 
 
 
 
  
 
 
 
 
 
 
  
 
 
 
 
 
  
 
) 
 
 
Note: The coordinates of the point A(   ) can also be derived by drawing 
perpendiculars from P, A and Q on the y-axis and proceeding as above. 
 
 
 
 
b. If the ratio in which A(   ) divides PQ is k : 1, then the coordinates 
of the point A will be 
 
 
Page 4


 
(Coordinate geometry is used to locate the position of a point on a plane with the 
help of a pair of coordinate axes) 
 
1. Coordinate Axes: Let      and      be two perpendicular lines 
intersecting at O. The point O is called the origin and      (x-axis) 
and      (y-axis) are called coordinate axes. 
 
 
 
2. The distance of a point from the x-axis is called its y-coordinate, or 
ordinate. 
  
3. The distance of a point from the y-axis is called its x-coordinate, or 
abscissa.  
 
 
 
4. Distance formula: 
 
a. Distance between two points [suppose, A( 
 
  
 
) and B( 
 
  
 
)] on a 
plane 
 
 
 
 
 
 
 
  
 
    
 
   
 
 
 
                                  ( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
                              v( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
Note: Since distance is always non-negative, we take only the positive value of the             
square root. 
 
 
b. Distance of a point A(   ) from the origin O(   ) on a plane. 
 
              v 
 
  
 
 
 
 
 
5. Section formula: 
a. The coordinates of the point A(   ) which divides the line segment 
PQ [where, P( 
 
  
 
) and Q( 
 
  
 
)], internally, in the ratio  
 
 
   
 
 are 
 
 
 
(
 
 
 
 
  
 
 
 
 
 
  
 
 
 
 
 
 
  
 
 
 
 
 
  
 
) 
 
 
Note: The coordinates of the point A(   ) can also be derived by drawing 
perpendiculars from P, A and Q on the y-axis and proceeding as above. 
 
 
 
 
b. If the ratio in which A(   ) divides PQ is k : 1, then the coordinates 
of the point A will be 
 
 
 
 
 
 
 
 
 
(
  
 
  
 
   
 
  
 
  
 
   
) 
 
 
c. If the ratio in which A(   ) divides PQ is 1 : 1, then the coordinates 
of the mid- point A will be (Also known as the Mid-point formula) 
 
 
 
(
   
 
    
 
   
 
   
 
    
 
   
)      (
 
 
  
 
 
 
 
 
  
 
 
) 
Page 5


 
(Coordinate geometry is used to locate the position of a point on a plane with the 
help of a pair of coordinate axes) 
 
1. Coordinate Axes: Let      and      be two perpendicular lines 
intersecting at O. The point O is called the origin and      (x-axis) 
and      (y-axis) are called coordinate axes. 
 
 
 
2. The distance of a point from the x-axis is called its y-coordinate, or 
ordinate. 
  
3. The distance of a point from the y-axis is called its x-coordinate, or 
abscissa.  
 
 
 
4. Distance formula: 
 
a. Distance between two points [suppose, A( 
 
  
 
) and B( 
 
  
 
)] on a 
plane 
 
 
 
 
 
 
 
  
 
    
 
   
 
 
 
                                  ( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
                              v( 
 
  
 
)
 
 ( 
 
  
 
)
 
 
 
Note: Since distance is always non-negative, we take only the positive value of the             
square root. 
 
 
b. Distance of a point A(   ) from the origin O(   ) on a plane. 
 
              v 
 
  
 
 
 
 
 
5. Section formula: 
a. The coordinates of the point A(   ) which divides the line segment 
PQ [where, P( 
 
  
 
) and Q( 
 
  
 
)], internally, in the ratio  
 
 
   
 
 are 
 
 
 
(
 
 
 
 
  
 
 
 
 
 
  
 
 
 
 
 
 
  
 
 
 
 
 
  
 
) 
 
 
Note: The coordinates of the point A(   ) can also be derived by drawing 
perpendiculars from P, A and Q on the y-axis and proceeding as above. 
 
 
 
 
b. If the ratio in which A(   ) divides PQ is k : 1, then the coordinates 
of the point A will be 
 
 
 
 
 
 
 
 
 
(
  
 
  
 
   
 
  
 
  
 
   
) 
 
 
c. If the ratio in which A(   ) divides PQ is 1 : 1, then the coordinates 
of the mid- point A will be (Also known as the Mid-point formula) 
 
 
 
(
   
 
    
 
   
 
   
 
    
 
   
)      (
 
 
  
 
 
 
 
 
  
 
 
) 
 
 
 
6. Area of a triangle: 
a. The area of a triangle formed by the points P( 
 
  
 
), Q( 
 
  
 
) and 
R( 
 
  
 
) is the numerical value of the expression 
 
 
 
 
 
 
 
[ 
 
( 
 
  
 
)  
 
( 
 
  
 
)  
 
( 
 
  
 
)] 
 
 
 
 
 
 
 
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