NCERT Solutions for Class 9 Maths Chapter 3: Coordinate Geometry

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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

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CBSE X Related Questions

1.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- 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
2.
If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is
- \(\frac{7}{2}\)
- \(\frac{6}{7}\)
- \(\frac{-7}{6}\)
- \(\frac{7}{6}\)
View Solution
3.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is
- \(-2\)
- \(\sqrt{\frac{8}{3}}\)
- \(1\)
- \(2\)
View Solution
4.
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is
- 34
- 43
- 38.5
- 41.5
View Solution
5.
It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?
- \(\frac{\text{Perimeter of } \triangle ABC}{\text{Perimeter of } \triangle EDF} = \frac{AB}{ED}\)
- \(\frac{AB}{ED} = \frac{AC}{EF}\)
- \(\angle A = \angle D, \angle C = \angle F\)
- \(\frac{AB + BC}{AC} = \frac{ED + DF}{EF}\)
View Solution
6.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is
- \(0\)
- \(\frac{80}{81}\)
- \(1\)
- \(\frac{82}{80}\)
View Solution

View All

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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.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

2.
If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

3.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

4.
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

5.
It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?

6.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is

Similar Mathematics Concepts

Comments

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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.Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number. Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

2.If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

3.If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

4.Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

5.It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?

6.For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.

2.
If the zeroes of the polynomial \(p(x) = 2x^2 - 7x + 6\) are \(\alpha\) and \(\beta\), then the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\) is

3.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

4.
Mean and Median of a frequency distribution are 43 and 40 respectively. The value of mode is

5.
It is given that \(\triangle ABC \sim \triangle EDF\). Which of the following is not true?

6.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is