Infographics Coordinate Geometry - (Maths) Class 10

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Coordinate Geometry
A powerful tool that connects algebra and geometry, helping you locate points, measure 
distances, and solve real-world problems using simple coordinates.
What is Coordinate Geometry?
Number Lines
Two perpendicular lines: 
x-axis (horizontal) and y-
axis (vertical) crossing at 
the origin (0,0)
Locating Points
Every point written as (x, 
y) where x is horizontal 
distance and y is vertical 
distance
René Descartes
Named after the brilliant 
mathematician who linked 
algebra with geometry
The Four Quadrants
The coordinate plane is divided into four regions called quadrants, each with unique sign 
patterns for coordinates.
Understanding Coordinates
x-coordinate (Abscissa)
Distance from the y-axis
Positive when right of y-axis
Negative when left of y-axis
Zero when on the y-axis
y-coordinate (Ordinate)
Distance from the x-axis
Positive when above x-axis
Negative when below x-axis
Zero when on the x-axis
Ex ample: Point (3, 22) means move 3 units right and 2 units down from the origin.
Distance Formula
Find the distance between any two points using coordinates. Based on Pythagoras theorem, 
this formula helps calculate exact lengths.
Formula
For points P(x¡, y¡) and Q(x¢, y¢):
d = ( x 2 x ) + ( y 2 y )
2 1
2
2 1
2
Solved Example
Distance between (1, 2) and (4, 6):
d = = (4 2 1) + (6 2 2)
2 2
 = 9 + 16
5 units
Section Formula
When a point P divides a line segment joining A(x¡, y¡) and B(x¢, y¢) in the ratio m:n 
internally, we can find P's coordinates using this powerful formula.
P ( x, y) = , (
m + n
m x + n x 
2 1
m + n
m y + n y 
2 1
)
01
Identify Points
Note coordinates of A and B, 
and ratio m:n
02
Apply Formula
Substitute values into section 
formula
03
Calculate
Find x and y coordinates of 
dividing point
Midpoint Formula: Special Case
When a point divides a segment equally (ratio 1:1), we get the simpler midpoint formula:
Midpoint Formula
M = , (
2
x + x 
1 2
2
y + y 
1 2
)
Simply average the x-coordinates and y-
coordinates!
Example
Midpoint of (2, 4) and (6, 8):
M = , = (
2
2 + 6
2
4 + 8
) (4, 6)
Area of Triangle
Calculate the area of a triangle when you know the coordinates of its three vertices, without 
measuring any sides directly!
Triangle Area Formula
For vertices A(x¡, y¡), B(x¢, y¢), C(x£, y£):
Area = # x ( y 2
2
1
1 2
y ) +
3
x ( y 2
2 3
y ) +
1
x ( y 2
3 1
y )#
2
The vertical bars | | mean take absolute value (always positive)
Real-Life Applications
Coordinate geometry isn't just theory4it powers technology and innovation all around us!
GPS Navigation
Your phone uses 
coordinates to find your 
location and calculate the 
shortest route to your 
destination
Engineering Design
Architects and engineers 
use coordinate systems 
to design buildings, 
bridges, and structures 
precisely
Computer Graphics
Animation and video 
games use coordinates to 
create and move 
characters and objects 
on screen
Robotics
Robots use coordinate geometry for path 
planning and navigation in warehouses 
and factories
Astronomy
Scientists plot positions of stars, planets, 
and galaxies using coordinate systems
Quick Tips to Remember
1
Coordinate Order
Always write as (x, y)4
horizontal first, then 
vertical. Remember: " x 
comes before y in the 
alphabet!"
2
Check Lengths
Use distance formula 
whenever you need to 
find the length between 
two points
3
Finding Points
Use section formula to 
find exact coordinates of 
dividing points on line 
segments
4
Quick Midpoint
For midpoint, just average the x's and 
average the y's4simple!
5
Practice Plotting
Draw and plot points regularly to 
understand quadrants and coordinate 
positions better
Why Learn Coordinate Geometry?
Connects Two Worlds
Links algebra and geometry for powerful problem-solving capabilities
Visual Understanding
Makes visualizing mathematical concepts and calculations much easier
Strong Foundation
Builds base for advanced mathematics, physics, engineering, and computer 
science
Develops Skills
Enhances logical thinking, spatial reasoning, and analytical abilities
Remember: 
Coordinate geometry is your mathematical GPS4it helps you navigate the plane of 
numbers with precision and confidence!
Quadrant I
(+x, +y)
Both coordinates positive
Quadrant II
(2x, +y)
x negative, y positive
Quadrant III
(2x, 2y)
Both coordinates negative
Quadrant IV
(+x, 2y)
x positive, y negative