These Class 9 Maths Notes and Chapter 1 Orienting Yourself The Use of Coordinates Class 9 Ganita Manjari Notes are designed according to the latest CBSE syllabus.
Class 9 Maths Chapter 1 Orienting Yourself The Use of Coordinates Notes
Class 9 Maths Ganita Manjari Chapter 1 Notes
Class 9 Orienting Yourself The Use of Coordinates Notes
→ Introduction: A system of coordinates is a structured framework (like the grid lines on a map or graph paper) that enables us to use numbers to describe the exact physical locations of points or objects.
→ The 2-D Cartesian Coordinate System: The two-dimensional coordinate system uses two lines at right angles to each other to mark points in two-dimensional space. It is written as 2-D space in short notation.
One line, usually we use, is a horizontal line called the x-axis and another line making a right angle with this line is the vertical line named as the y-axis.
The point at which these axes intersect is called the origin with its coordinates 0(0, 0).
The first number in the coordinates represents the x-coordinate known as the abscissa and the second number in the coordinates represents the y-coordinate known as the ordinate.
Plural form of axis is axes, which is used to represent the coordinates axes altogether.
Distances from O are marked off in equal units, on both the axes.
Distances to the right of O or upwards from O are considered positive and distances to the left of O or downwards from O are considered negative.
Following figure represents the coordinates system:
The axes divide the plane of the graph into four equal parts known as Quadrants.
In the First Quadrant coordinates are of the form (+, +), in the Second Quadrant (-, +), in the Third Quadrant (-, -) and in the Fourth Quadrant (+, -).
→ Cartesian Plane and The Coordinate Axes: The plane is called the Cartesian plane, the coordinate plane or the xy-plane and the lines are called the coordinate axes. The horizontal line is called the x-axis and the vertical line is called the y-axis.
→ Quadrants and The Origin: The coordinate axes divide the plane into four parts called quadrants. The point of intersection of the axes is called the origin.
→ Coordinates of a Point: The distance of a point from the y-axis is its x-coordinate and the distance of the point from the x-axis is its y-coordinate. If the x-coordinate of a point is x and the y-coordinate is y, then (x, y) are called the coordinates of the point.
If x = y, then (x, y) = (y, x). If x + y, then (x, y) f (y, x).
→ Coordinates of the Points lying on the Axes: The coordinates of a point on the x-axis are of the form (x, 0), and those of the points on the y-axis are of the form (0, y).
Since, origin lies on the intersection of both the axes, thus the coordinates of the origin are (0, 0).
→ Distance Between Two Points in 2-D Plane:
AB = \(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
The above formula is by the Baudhdyana-Pythagoras Theorem.
→ The distance between points (x1, y) and (x2, y) is the absolute value |x2 – x1|
→ The distance between points (x, y1) and (x, y2) is the absolute value |y2 – y1| of the difference between y1 and y2.
→ Uses of distance formula:
- To find the distance between any two given points.
- To show three points as collinear points.
- To identify various geometrical shapes, like Scalene Triangle, Isosceles Triangle, Equilateral Triangle, Square, Rectangle, Parallelogram, Rhombus, etc.
- To find the radius of a circle if its centre and a point on its circumference are given.
- To prove some important geometrical concepts like ‘the line joining the mid-points of any two sides of a triangle is half of the third side of that triangle’, ‘diagonals of a square or that of a rectangle are equal but they are unequal in a parallelogram’