Points to Remember: Coordinate Geometry

Points to Remember: Coordinate Geometry | Mathematics (Maths) Class 10 PDF Download

``` Page 1

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
2
nd
3
rd
4
th
(-, +)
=
=
=
Coordinate Geometry
Page 2

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
2
nd
3
rd
4
th
(-, +)
=
=
=
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-
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
?
?
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.
?
?
```

Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

FAQs on Points to Remember: Coordinate Geometry - Mathematics (Maths) Class 10

 1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using the coordinate system. It involves assigning numerical values, called coordinates, to points on a plane or in space, which helps in analyzing and solving various geometric problems.
 2. How can coordinate geometry be applied in real life?
Ans. Coordinate geometry finds practical applications in various fields. For example, it is used in navigation systems to determine the location of vehicles or objects. It also plays a crucial role in computer graphics, where it is used to create and manipulate images on a screen. Additionally, coordinate geometry is utilized in surveying land and designing blueprints for construction projects.
 3. What are the different types of coordinates used in coordinate geometry?
Ans. In coordinate geometry, there are mainly two types of coordinates used: Cartesian coordinates and polar coordinates. Cartesian coordinates represent points using the distance from the origin along the x-axis (horizontal) and y-axis (vertical). On the other hand, polar coordinates represent points using the distance from the origin and the angle formed with a reference line.
 4. How do you find the distance between two points in coordinate geometry?
Ans. The distance between two points in coordinate geometry can be found using the distance formula. The formula is derived from the Pythagorean theorem and is given as follows: Distance = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
 5. Can coordinate geometry be used to solve equations and inequalities?
Ans. Yes, coordinate geometry can be used to solve equations and inequalities. By representing equations and inequalities graphically on a coordinate plane, we can analyze their solutions and understand their behavior. This graphical representation allows us to visually interpret the solutions and make calculations easier.

Mathematics (Maths) Class 10

116 videos|420 docs|77 tests

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