NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry

Content Curator

The NCERT Solutions for class 9 Maths Chapter 3 Coordinate Geometry have been provided in the article below. Coordinate Geometry deals with geometrical problems solved using coordinate systems and points.

Class 9 Maths Chapter 3 Coodinate Geometry belongs to Unit 3 Coordinate Geometry having a weightage of 04 in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 3 cover the following important concepts:

Distance Formula of coordinate geometry
Section Formula of coordinate geometry
Ordinate
Quadrant
Cartesian System

Download: NCERT Solutions for Class 9 Maths Chapter 3 pdf

NCERT Solutions for Class 9 Maths Chapter 3

The Chapter 3 Class 9 Maths are given below:

NCERT Solutions

Important Topics in Class 9 Maths Chapter 3 Coordinate Geometry

Important Topics in Class 9 Maths Chapter 3 Coordinate Geometry are elaborated below:

Distance Formula of Coordinate Geometry

Distance formula of coordinate geometry, derived from the Pythagoras Theorem, is used to determime the distance between any 2 given points. These points are usually located on an x-y coordinate plane. Distance Formula of coordinate geometry can be written as, AB = √[(x2-x1)²+(y2-y1)²]

Example: Consider coordinate A (-4,0) and B (0,3). With the given coordinates, determine the distance between these two points.

Solution: Considering the coordinates ofA = (-4,0) = (x1, y1)
And the coordinates of B = (0,3) = (x2,y2)
Now by using Distance Formula, we can get,
AB = √{(x2-x1)²+(y2-y1)²} = √{[0-(-4)]²+ (3-0)²}
= √(4²+3²)} = √(16+9) = √25
= 5 units

Section Formula of Coordinate Geometry

Section Formula helps to determine the coordinates of a point that assists division of the line joining two points in a ratio. The equation occurs either internally or externally.

Section Formula of Coordinate Geometry can be classified into two parts:

Internal Section Formula: $P(x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})$
External Section Formula: $P(x,y) = (\frac{mx_2-nx_1}{m-n} , \frac{my_2-ny_1}{m-n})$

Ordinate

Ordinate represents the coordinate values present on the y-axis on a coordinate system. It is the second component of an ordered pair.

Example: What will be the abscissa and ordinate of a point with coordinates (8,12)?

Solution: The coordinates of (8, 12) are:
Abscissa: 12
And, Ordinate: 8

Quadrant

Quadrants are the parts that form when two coordinate axes of a plane tend to intersect with one another at an angle of 90 degree. The intersection these two lines experience is called a point of reference.

Example: Highlight the quadrants where coordinate points (-2,7) take place?

Solution: (-2,7) falls in the second quadrant. Here, the value of the x axis becomes negative.

Cartesian System

Cartesian System, derived from the number line, is used to label points in a plane. The cartesian form is derived from the number line. It has two perpendicular lines named as X-axis and Y-axis.

Important points to remember in Cartesian System:

The point of intersection of both the axes is called the origin. It has coordinates (0, 0).
An infinite number of points can be plotted on a cartesian coordinate plane.
Points that fall on any of the number lines don’t belong to any quadrant.

NCERT Solutions for Class 9 Maths Chapter 3 Exercises:

The detailed solutions for all the NCERT Solutions for Coordinate Geometry under different exercises are:

Also Read:

Unit Related Topics
Equation of a Line Formulas	Centroid formula	Midpoint formula
Centroid of a triangle	Important MCQs on Coordinate Geometry	Slope Formula

Check out:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.
View Solution
2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$
View Solution
3.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.
View Solution
4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.
View Solution
5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
6.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
View Solution

View All

Similar Mathematics Concepts

Midpoint Formula: Midpoint Definition, Theorem, Solved Examples

Centroid: Definition, Types, Theorem, Properties, Formulas

NCERT Solutions for class 10 Maths chapter 7: Coordinate Geometry

NCERT Solutions for Class 10 Maths: Chapter-wise Solutions and Important Topics

Coordinate Geometry MCQs

Point of Intersection Formula: Gradient & Point Slope

Important MCQs on Coordinate Geometry with Explanation

Perpendicular Distance of a Point from a Plane Formula

Coordinate Geometry: Important Questions

NCERT Solutions for Class 10 Maths Chapter 7 Exercise 7.1

Mathematics Preparation Guides

Statistics: Mean, Median, Variance and Cumulative Frequency Curve

Remainder Theorem: Definition, Steps & Examples

Angle Formula: Definition, Different Types, Solved Example

Trapezoids: Isosceles, Scalene Properties, Area, Properties, Examples

Quadrilateral Angle Sum Property: Theorem, Types & Example

Frequency Polygons: Steps, Formula & Examples

Area of Parallelogram: How to Calculate Area of Parallelogram?

Congruence of Triangles: SSS, SAS, ASA & RHS Rules

Quadrilateral Formulas: Types and Properties

Properties of Triangle: Types, Formulas & Examples

Class 9 Maths MCQ: Chapter-wise with Solutions

Properties of Parallel Lines: Transitive & Symmetric Properties

Isosceles triangle: Types, Properties, Angles & Examples

Operations on Rational Numbers:Rules, Properties & Examples

Addition and Subtraction of Integers: Rules & Examples

Scalene Triangle: Types, Formulas, Properties & Examples

Quadrant: Types, Sign Convention & Examples

Rationalize the Denominator: Explanation and Solved Examples

Area of a Kite: Formula, Derivation & Examples

Volume of a Pyramid: Formula and Solved Example

Mathematics NCERT Solutions

Linear Equation in Two Variables: Graph, Elimination and Substitution

Types of Triangles: Important Terms, Scalene, Acute, and Obtuse Triangle

Formula Of Perimeter Shapes

Sphere Formula: Diameter, Surface Area and Volume

Ordinate: Abscissa, Plotting Ordinates, Relation, Solved Examples

Integers as Exponents: Explanation, Rules and Method of Solving

Central Tendency: Definition, Methods and Sample Questions

Line Segment: Definition, Measurement and Examples

Line, Line Segment and Ray: Differentiation and Sample Questions

Area of Equilateral Triangle, Perimeter & Altitude Formulas

NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3

Important Topics in Class 9 Maths Chapter 3 Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3 Exercises:

CBSE X Related Questions

1.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3

Important Topics in Class 9 Maths Chapter 3 Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3 Exercises:

CBSE X Related Questions

1.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

2.Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

4.In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

2.
Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

3.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

4.
In the given figure, $AB \parallel DE$ and $AC \parallel DF$. Show that $\Delta ABC \sim \Delta DEF$. If $BC = 10\text{ cm}$, $EB = CF = 5\text{ cm}$ and $AB = 7\text{ cm}$, then find the length $DE$.

5.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

6.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.