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Ever been lost and wished someone could drop a pin for you? Well, maths solved that problem long before Google Maps!
That’s exactly what this chapter from Class 9 Maths Syllabus Coordinate Geometry helps us do - find the location of any point on a flat surface using just two numbers: x and y. Think of it as the GPS of mathematics.
In this chapter, you’ll learn about the Cartesian Plane, axes, quadrants, and how to locate points easily - all explained in a simple, student-friendly way.
Class 9 Coordinate Geometry Notes PDF
This chapter introduces you to the x-axis and y-axis, the Cartesian system, and plotting points on a graph. It might sound new, but once you get the hang of it, it's really fun and useful, especially in upper-level classes and even in real life like maps and GPS!
These notes have been made in an easy and concise format so that you can revise swiftly, comprehend easier, and get higher marks in your board exams. Be it your boards or any class test, these PDF notes will support you.
What is Coordinate Geometry?
Coordinate Geometry is a branch of mathematics that deals with the study of geometric figures using numbers and algebraic methods. It helps us locate the exact position of a point on a plane by using a pair of numbers called coordinates.
This system uses two perpendicular number lines known as the x-axis (horizontal) and the y-axis (vertical). The point where both axes intersect is called the origin and is represented by (0, 0).
Each point in the plane is represented by an ordered pair (x, y), where the x-coordinate shows the horizontal distance from the y-axis and the y-coordinate shows the vertical distance from the x-axis.
Cartesian Coordinate System
The Cartesian coordinate system is formed by two mutually perpendicular number lines:
- X-axis (horizontal line)
- Y-axis (vertical line)
These axes divide the plane into four regions called quadrants. The point where both axes intersect is called the origin.
Axes in Coordinate Geometry
X-axis
- Horizontal line
- Values on the right are positive
- Values on the left are negative
- Any point on the x-axis has y = 0
Example: (4, 0), (–3, 0)
Y-axis
- Vertical line
- Values above the origin are positive
- Values below the origin are negative
- Any point on the y-axis has x = 0
Example: (0, 5), (0, –2)
Coordinates of a Point
The position of a point in a plane is written as an ordered pair (x, y):
- x-coordinate (abscissa): distance from the y-axis
- y-coordinate (ordinate): distance from the x-axis
Example
- Point A (2, - 3)
- x = 2 (right of y-axis)
- y = -3 (left of y-axis)
Quadrants
Plotting a Point on the Cartesian Plane
Steps to plot a point (x, y):
- Start from the origin (0, 0)
- Move x units along the x-axis
- Right if x is positive
- Left if x is negative
- From that point, move y units parallel to the y-axis
- Up if y is positive
- Down if y is negative
- Mark the point and label it
Collinearity Condition
If three points A, B and C are collinear and B lies between A and C, then,
- AB + BC = AC. AB, BC, and AC can be calculated using the distance formula.
- The ratio in which B divides AC, calculated using the section formula for both the x and y coordinates separately, will be equal.
- The area of a triangle formed by three collinear points is zero.
Some Solved Examples
Ex 1: If a point's abscissa is 6 and its ordinate is 2 ,the point’s co-ordinates are expressed as (6,2).
Solution: Assume that A is a point on the plane. AC XOX' ⊥ and AB YOY' ⊥ should be drawn.
The ordered pair (x,y) is said to define the point A if OC = x and OB = y
A's Cartesian coordinates are also known as x and y.
As a result, we can associate an ordered pair (x,y) of real numbers with each point in the plane.
We can, on the other hand, map a point in the plane given an ordered pair of numbers
Ex 2: Determine the distance between the pair of points (a, b) and (-a, -b)
Solution: Let the given points be A(a, b) and B(-a, -b)
We know that the distance formula is:
AB = √[(x2-x1)2+(y2-y1)2]
(x1, y1) = (a, b)
(x2, y2) = (-a, -b)
Now, substitute the values in the distance formula, we get
AB = √[(-a-a)2+(-b-b)2]
AB = √[(-2a)2 + (-2b)2]
AB = √[4a2 + 4b2]
AB = √[4(a2+b2)]
AB = √4. √[a2+b2]
AB = 2.√[a2+b2].
Hence, the distance between two points (a, b) and (-a, -b) is 2√[a2+b2].
Ex 3: Find the area of the triangle ABC whose vertices are A(1, 2), B(4, 2) and C(3, 5).
Solution: Using the formula A = (1/2) [x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)]
A = (1/2) [x1 (y2 – y3) + x2 (y3 – y1) + x3(y1 – y2)]
A = (1/2) [1(2 – 5) + 4(5 – 2) + 3(2 – 2)]
A = (1/2) [-3 + 12]
Area = 9/2 square units.
Therefore, the area of a triangle ABC is 9/2 square units.
FAQs
Q1. What is coordinate geometry?
Ans: Coordinate geometry is the study of geometry using a coordinate system. It helps us find the position of a point on a plane using numbers.
Q2. What is the Cartesian plane?
Ans: A plane divided into four quadrants by a horizontal (x-axis) and vertical (y-axis) line is called a Cartesian plane.
Q3. What is the origin?
Ans: The point where the x-axis and y-axis intersect is called the origin. Its coordinates are (0, 0).
Q4. What are coordinates of a point?
Ans: Coordinates are a pair of numbers that show the exact position of a point in the Cartesian plane in the form (x, y).
Q5. What is the x-coordinate and y-coordinate?
Ans: x-coordinate (abscissa) tells us the horizontal position. y-coordinate (ordinate) tells us the vertical position.
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