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.
The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is
- 2
- \(-6\)
- \(-2\)
- 6
View Solution
2.
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
3.
Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is
- \(10^{\circ}\)
- \(60^{\circ}\)
- \(45^{\circ}\)
- \(100^{\circ}\)
View Solution
4.
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
5.
If for a data, median is 5 and mode is 4, then mean is equal to :
- 7
- 11
- \(\frac{11}{2}\)
- \(\frac{14}{3}\)
View Solution
6.
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

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.
The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is

2.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is

3.
Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is

4.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

5.
If for a data, median is 5 and mode is 4, then mean is equal to :

6.
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

Similar Mathematics Concepts

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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.The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is

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

3.Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is

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

5.If for a data, median is 5 and mode is 4, then mean is equal to :

6.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

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The value of k for which sum of the zeroes of the polynomial \(p(x) = 3x^2 - kx + 6\) is 2, is

2.
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is

3.
Arc \(PQ\) subtends an angle \(\theta\) at the centre of the circle with radius \(6.3 \text{ cm}\). If \(\text{Arc } PQ = 11 \text{ cm}\), then the value of \(\theta\) is

4.
If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of k is

5.
If for a data, median is 5 and mode is 4, then mean is equal to :

6.
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