Points to Remember: Coordinate Geometry Notes | EduRev

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Class 10 : Points to Remember: Coordinate Geometry Notes | EduRev

 Page 1


Coordinate 
Geometry 
Page 2


Coordinate 
Geometry 
Distance Formula :
1 1 2 2
Distance between two points (x ,y ) & (x ,y )
Section Formula :
Internal division
P (x, y) =
m
1
x
2
 + m
2
x
1
m
1
 + m
2
m
1
y
2
 + m
2
y
1
m
1
 + m
2
{
,
}
External division
m
1
x
2
 - m
2
x
1
m
1
 - m
2
{
,
m
1
y
2
 - m
2
y
1
m
1
 - m
2
}
Mid point
{
,
}
P (x, y) =
x
1
 + x
2
2
y
1
 + y
2
2
Area of triangle :
A = {x
1
 (y
2
- y
3
) + x
2
 (y
3
- y
1
) + x
3
 (y
1
- y
2
)}
1
2
D = v (x
1
-x
2
)
2
 + (y
1
-y
2
)
2
D = v (x
2
-x
1
)
2
 + (y
2
-y
1
)
2
or
P (x, y) =
Coordinate axes
x axis
y axis
.
.
.
.
(+, -)
(-, -)
(+, +)
1
st
 Quadrant
2
nd
 Quadrant
3
rd
 Quadrant
4
th
 Quadrant
(-, +)
=
=
=
COORDINATE GEOMETRY 20
Coordinate Geometry
Page 3


Coordinate 
Geometry 
Distance Formula :
1 1 2 2
Distance between two points (x ,y ) & (x ,y )
Section Formula :
Internal division
P (x, y) =
m
1
x
2
 + m
2
x
1
m
1
 + m
2
m
1
y
2
 + m
2
y
1
m
1
 + m
2
{
,
}
External division
m
1
x
2
 - m
2
x
1
m
1
 - m
2
{
,
m
1
y
2
 - m
2
y
1
m
1
 - m
2
}
Mid point
{
,
}
P (x, y) =
x
1
 + x
2
2
y
1
 + y
2
2
Area of triangle :
A = {x
1
 (y
2
- y
3
) + x
2
 (y
3
- y
1
) + x
3
 (y
1
- y
2
)}
1
2
D = v (x
1
-x
2
)
2
 + (y
1
-y
2
)
2
D = v (x
2
-x
1
)
2
 + (y
2
-y
1
)
2
or
P (x, y) =
Coordinate axes
x axis
y axis
.
.
.
.
(+, -)
(-, -)
(+, +)
1
st
 Quadrant
2
nd
 Quadrant
3
rd
 Quadrant
4
th
 Quadrant
(-, +)
=
=
=
COORDINATE GEOMETRY 20
Coordinate Geometry
To check whether the three points form an isosce-
les triangle or an equilateral triangle, nd out the 
distance between all the three points and if the 
two sides or three sides are same, we can con-
clude the answer respectively.
 To check whether the three points A, B and C are 
collinear either show  AB + BC = AC or you can prove 
it by calculating the area of a triangle formed by 
these three points is zero.
 To calculate the area of any quadrilateral, divide 
it into two triangles then nd the area of individual 
triangle and add them. 
?
?
 Please try to remember all the properties of 
quadrilaterals and triangles, for the questions which 
ask to check whether the points form any geometrical 
shape or not. 
?
?
PLEASE KEEP IN MIND
Scan the QR Codes to watch our free videos
Introduction to
Coordinate Geometry
Distance formula
COORDINATE GEOMETRY 21
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