Courses

# Points to Remember: Coordinate Geometry Notes | EduRev

## 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
```
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

1 videos|13 docs

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;