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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1.
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