Coordinate geometry explains geometry using numbers instead of drawings. It places points on a Cartesian plane using ordered pairs of real numbers. Each point depends on an x coordinate and a y coordinate measured from the origin along the X axis and Y axis. This method allows students to measure distance, locate positions, divide line segments, and verify shapes using calculation rather than visual judgment. In CBSE Class 10 Maths, coordinate geometry forms a core part of analytical problem solving and directly supports topics such as linear equations, trigonometry, and mensuration.

In this blog, you will learn the important coordinate geometry formulas for Class 10 Maths and understand what each formula helps you find.

Key CBSE Class 10 Maths Coordinate Geometry Formulas

Coordinate geometry converts geometric problems into algebraic calculations on a Cartesian plane. The following formulas help you find distances, locate division points, and calculate areas using coordinate values. 

1. Distance Formula (Length Between Two Points)

What it finds:
Distance between any two points on the plane.

Formula:
D = √[(x₂ − x₁)² + (y₂ − y₁)²]

How to use it:
Substitute coordinates (x₁, y₁) and (x₂, y₂) into the formula and evaluate the square root.
Used for perimeter, length, and position problems.

2. Section Formula (Divide Line Segment in Ratio)

The section formula gives coordinates where a point divides a line segment in a given ratio.

Internal Division (m : n):
(x, y) = ((m·x₂ + n·x₁) / (m + n), (m·y₂ + n·y₁) / (m + n))

External Division (m : n):
(x, y) = ((m·x₂ − n·x₁) / (m − n), (m·y₂ − n·y₁) / (m − n))

Use:
Find a point that splits a line segment either inside (between) the endpoints or outside them. 

3. Midpoint Formula (Equal Division Point)

What it finds:
Point exactly halfway between two coordinates.

Formula:
Midpoint of (x₁, y₁) and (x₂, y₂) = ( (x₁ + x₂)/2, (y₁ + y₂)/2 )

Use:
Quickly locate the center of a segment without using ratios.

4. Area of a Triangle Using Coordinates

What it finds:
The area enclosed by a triangle formed by three points.

Determinant-based Formula:
Area = ½ | x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂) |

Use:
Helps check whether three points form a triangle or are collinear (zero area).

Applications of Coordinate Geometry Formulas

Coordinate geometry formulas solve real location and distance problems using numerical data.

• GPS systems use coordinate grids based on latitude and longitude to determine exact positions on Earth.
• Astronomers calculate distances between planets and stars using coordinate based models.
• Digital maps rely on Cartesian coordinate systems to display locations on screens.
• Two dimensional and three dimensional coordinate systems help define shape, position, and direction using x and y values.

Tips to Memorize and Use These Formulas

Follow these study tactics to learn formulas faster:

1. Understand the meaning of each formula before memorising.
2. Learn derivations; this helps preventing sign and substitution mistakes.
3. Practice with many examples; varied questions reinforce formula usage.
4. Write formulas in a chart organized by purpose (distance, division, area) for quick recall.

Example: Finding Distance Between Two Points

Question:
Find the distance between the points A(2, −3) and B(6, 3).

Step 1: Identify the coordinates
A(x₁, y₁) = (2, −3)
B(x₂, y₂) = (6, 3)

Step 2: Apply the distance formula

Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]

Step 3: Substitute the values

Distance = √[(6 − 2)² + (3 − (−3))²]
Distance = √[(4)² + (6)²]
Distance = √(16 + 36)

Step 4: Simplify

Distance = √52
Distance = 2√13 units

Answer:
The distance between points A and B equals 2√13 units.