Class 10 Coordinate Geometry: Notes, Formulas & Solved Examples
Class 10 coordinate geometry is an important chapter in CBSE Maths that focuses on understanding geometric concepts using algebra. With clear formulas, step-by-step methods, and regular practice, students can score full marks in this chapter.
This blog provides coordinate geometry notes for Class 10, including important formulas, solved examples, and exam tips to help students prepare confidently.
What Is Coordinate Geometry?
Coordinate geometry is a branch of mathematics that studies geometric figures using numbers and algebraic methods. In coordinate geometry class 10, points are represented on a plane using ordered pairs, making it easier to calculate distances, areas, and ratios.
In class 10 maths coordinate geometry, students learn how algebra helps solve geometry problems accurately and logically.
Cartesian Plane and Coordinates
- X-axis: Horizontal line on the plane
- Y-axis: Vertical line on the plane
- Origin (0,0): Point where X-axis and Y-axis intersect
- Quadrants:
- Quadrant I: (+, +)
- Quadrant II: (−, +)
- Quadrant III: (−, −)
- Quadrant IV: (+, −)
Each point is written as (x, y) where x is the x-coordinate and y is the y-coordinate.
Important Topics in Class 10 Coordinate Geometry
Class 10 coordinate geometry mainly focuses on formula-based numerical problems that are easy to score with practice.
Chapter Overview
- Distance Formula
- Section Formula (Internal & External Division)
- Area of Triangle
These topics form the core of coordinate geometry class 10 questions in CBSE board exams.
Distance Formula (Coordinate Geometry Class 10)
The distance formula is one of the most important coordinate geometry formulas used to find the distance between two points on a plane.
Distance Formula
For points A (x₁, y₁) and B (x₂, y₂):
Distance= 𝑑=(𝑥2−𝑥1)2+(𝑦2−𝑦1)2√
This formula is widely used in coordinate geometry class 10 formulas.
Example (Distance Formula):
Find the distance between A (2, 3) and B (6, 7).
Step 1: Identify values
x₁ = 2, y₁ = 3
x₂ = 6, y₂ = 7
Step 2: Apply the formula
(6−2)2+(7−3)2−−−−−−−−−−−−−−−√=16+16−−−−−−√=32−−√=42–√6−2)2+(7−3)2=16+16=32=42
Section Formula (Internal & External Division)
The section formula helps find the coordinates of a point dividing a line segment in a given ratio. It is a key part of coordinate geometry class 10 formulas.
Internal Division Formula
If point P divides AB internally in the ratio m:n:
P(mx2+nx1m+n,my2+ny1m+n)Pmx2+nx1m+nmy2+ny1m+n
External Division Formula
If point P divides AB externally in the ratio m:n:
P(mx2−nx1m−n,my2−ny1m−n)Pmx2−nx1m−nmy2−ny1m−n
Solved Example (Section Formula)
- Find the coordinates of a point dividing A(1,2) and B (5,6) internally in the ratio 1:1.
P(1(5)+1(1)2,1(6)+1(2)2) P1(5)+1(1)21(6)+1(2)2
= (3,4)
Area of Triangle in Coordinate Geometry
The area of triangle in coordinate geometry is one of the most important and high-weightage topics in CBSE exams.
Area of Triangle Formula
If the vertices of a triangle are A (x₁, y₁), B (x₂, y₂), and C (x₃, y₃), then the area of triangle formula in coordinate geometry is:
Area =½ |x₁ (y₂ − y₃) + x₂ (y₃ − y₁) + x₃ (y₁ − y₂) |
Condition for Collinearity
If the area of the triangle is zero, then the three points are collinear (lie on the same straight line).
Solved Example (Area of Triangle)
Question: Find the area of the triangle with vertices (1,1), (2,4), and (5,3).
Answers: ½ |1 (4 − 3) + 2 (3 − 1) + 5 (1 − 4) | = ½ |1+4-15| = ½ (10) = 5 Square units
All Coordinate Geometry Formulas – Class 10
Here is a quick revision list of coordinate geometry formulas:
Distance Formula:
(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−−√x2−x1)2+(y2−y1)2
Section Formula:
Internal and External division formulas
Internal Formula:
P(mx2+nx1m+n,my2+ny1m+n)Pmx2+nx1m+nmy2+ny1m+n
External Formula:
P(mx2− nx1m−n,my2−ny1m−n)Pmx2− nx1m−nmy2−ny1m−n
Area of Triangle Formula:
12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣∣∣12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣
These coordinate geometry class 10 formulas are essential for scoring full marks.
Important Solved Examples – Class 10 Coordinate Geometry
Coordinate geometry class 10 solutions usually include:
- Finding distances between points
- Applying section formula for given ratios
- Finding the area of triangles
Practicing these examples helps students understand CBSE question patterns.
Common Mistakes Students Make
While preparing class 10 coordinate geometry, students often:
- Substitute wrong values in formulas
- Confuse distance and section formulas
- Make calculation errors
- Skip steps in answers
Avoiding these mistakes improves accuracy and confidence.
How to Score Full Marks in Class 10 Coordinate Geometry
To score full marks in coordinate geometry class 10:
- Memorize all formulas
- Practice numericals daily
- Write proper steps in exams
- Revise formulas before tests
Personalized academic guidance helps student’s clear doubts quickly and strengthen weak areas.
Frequently Asked Questions (FAQs) – Class 10 Coordinate Geometry
- Is coordinate geometry difficult for Class 10?
A. No. With regular practice and formula clarity,class 10 coordinate geometry is easy and scoring.
2. Which formula is most important in coordinate geometry?
A. The distance formula, section formula, and area of triangle in coordinate geometry are the most important.
3. How many marks does coordinate geometry carry in Class 10?
A. Coordinate geometry carries significant weightage in CBSE Maths exams.
4. Is area of triangle important for board exams?
A. Yes. Questions based on the area of triangle formula in coordinate geometry arefrequently
5. How can I practice coordinate geometrynumericals?
A. Practice NCERT questions, solve previous year papers, and revise formulas regularly.
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