Monday, 12 June 2017

Co-ordinate Geometry I- Introduction to Co-ordinate Geometry for SSC Exams

Co-ordinate Geometry Problems are asked in SSC CGL and other SSC Exams, which makes it an important topic for you. Read on for an introduction to co-ordinate geometry along a list of important terms and understanding of the Cartesian system.

Co-ordinate Geometry
Questions from co-ordinate geometry are asked in all SSC Exams which makes it imperative for you understand the basics of this topic to solve co-ordinate geometry problems. Co-ordinate Geometry or Analytic Geometry is a way to study geometry through a co-ordinate system. A co-ordinate system is a system, where we use a set of values or numbers to uniquely locate the position of the point in the given plane or space. There different kinds of systems used in co-ordinate geometry, but the most common one is called the Cartesian System.
So in this series on co-ordinate geometry we start with discussing- what is co-ordinate geometry, the important terms in co-ordinate geometry and some concepts that will help you solve co-ordinate geometry problems.


What is Co-ordinate Geometry?

In the Cartesian co-ordinate system in co-ordinate geometry, the plane is described with the help of two mutually perpendicular lines. Any point in this plane can be easily located with the help of two numerical values know as co-ordinates. These points denote the distance of the point from these two mutually perpendicular points.

Important Terms in Cartesian Co-ordinate Geometry

Before we move ahead with understanding the concepts in Cartesian system of co-ordinate geometry, we need to discuss some important terms that constitute co-ordinate geometry.

Co-ordinates- A point on this plane is represented by a set of co-ordinates that determine its distance from the two lines. It is a pair of digits separated by a comma.

Origin (O)- The point in the centre where the two lines, one horizontal and one vertical, intersect is known as the origin. It is represented by the letter ‘O’ and is represented by the co-ordinates (0,0).

Plane (P)- A flat, two dimensional surface that extends infinitely, where any point can be plotted with the help of co-ordinates is called a plane. It is represented by the letter ‘P’.

Co-ordinate Axis – The two lines, horizontal and vertical, from which the distance of the points in the plane is measured, are called the co-ordinate axis.

Horizontal Axis (X)- The horizontal line that extends up to infinity from left and right, is called the horizontal axis or x axis. It is represented by the letter ‘X’.

Vertical Axis (Y)- The vertical line that extends up to infinity from top and bottom, is called the vertical axis or y axis. It is represented by the letter ‘Y’.

Quadrants (Q)- The two mutually perpendicular axis divide the plan in four parts. Each of this region/ part is known as a quadrant. It is represented by the letter ‘Q’.

Quadrant 1 (Q1)- In Quadrant 1, x-axis is positive and y-axis is positive. It is represented by Q1.

Quadrant 2 (Q2)- In Quadrant 2, x-axis is negative and y-axis is positive. It is represented by Q2.

Quadrant 3 (Q3)- In Quadrant 3, x-axis is negative and y-axis is negative. It is represented by Q3.

Quadrant 4 (Q4)- In Quadrant 4, x-axis is positive and y-axis is negative. It is represented by Q4.

Ordered Pair (x, y)- An ordered pair represents a particular point of the plane in a quadrant. It is written as (x, y), where ‘x’ represents the value on the x-axis and ‘y’ represents the value on the y-axis.

Abscissa (x)- In a ordered pair, ‘x’ is the abscissa, it represents the distance of a point from the y-axis and is measured parallel to the x-axis.

Ordinate (y)- In a ordered pair, ‘y’ is the ordinate, it represents the distance of a point from the x-axis and is measured parallel to the y-axis.

Understanding the Cartesian System in Co-ordinate Geometry

Now that we have discussed some important terms in co-ordinate geometry, let’s move on to understanding some key concepts. Understanding of these concepts of co-ordinate geometry is essential for solving problems.

The origin is represented by (0, 0) as it is at 0 units distance from both the y-axis and the x-axis. Similarly, if we consider an ordered pair A(2, 0), here the distance from the y-axis is 2 but there is no distance from the x-axis. The point is on the x-axis itself. Vice Versa, in the ordered pair B(0, 6), the distance from y-axis is zero as the point is on the y axis.

Point M in Q2 represents the ordered pair (-4, 3) where the numbers denote the distance from the y-axis and x-axis respectively. In Q3 the ordered pair (-3, -1) is represented by N where -3 and -1 represent the distance from the y-axis and the x-axis. R is Q4 is represented by (3, -6) where the distance from the y-axis and the x-axis is 3 and 6 respectively. You must remember that the signs in ordered pairs merely indicate the quadrant the point is in. This is how any point is represented on the plane in Cartesian form in co-ordinate geometry.
Co-ordinate Geometry
Stay tuned for the next blog where we discuss questions in co-ordinate geometry that are asked in competitive exams.
Remember to write in the comments how this blog helped you understand the basics of co-ordinate geometry.
Co-ordinate Geometry

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