cartesian coordinates

A Coordinate plane is two-dimensional surface that is formed by two number lines. One number line is horizontal and is called X-axis. Another number line is vertical and is called Y-axis. Both the axis intersect at the origin. Origin is a point where zero of both the number line lies is found.

We use coordinate plane to graph points, lines and other pictures.

What we will learn:

• What is a coordinate plane?
• How to represent a point on a coordinate plane?
• What are quadrants?

What is  the coordinate axis?

A coordinate plane has one horizontal axis, the x-axis and one vertical axis, the y-axis

What is Origin?

The point at which X and Y axis intersect is called the Origin.

Cartesian Coordinates are also called Rectangular Coordinates. Cartesian Coordinates are a pair of numbers that specify the distance from the coordinate axis. We can locate any point on the coordinate plane using ordered pair of numbers. We call ordered pair as coordinates of the point. They are called ordered pair because the order of two numbers is important.

• To indicate something on a plane, we need horizontal measurement (X) and vertical measurement (Y). The reference point from which we measure is called origin represented by 'O'. It is the point of intersection of the horizontal line (X axis) and the vertical line (Y axis).
• Horizontal line, X axis: The numbering starts at the origin, with its value as 0. As the value of X increases the dot is placed farther to the right. So, 4 on the X- axis is 4 positions to the right of the origin. When X decreases we move further to the left
• Vertical line, Y axis: The numbering starts at the origin, with its value as 0 and increases as we move upwards. So, 4 on the Y-axis is 4 positions above the origin. When Y decreases, the point moves further down.
• The X and Y axes divide the space into 4 regions and are called 'Quadrants'. Quadrant I, II, III and IV (in roman numerals)

Writing Coordinates

Coordinates are always written in a certain order. The horizontal distance,  then the vertical distance.  They are separated by a comma and closed in parentheses.

(3,2)

means 3 unit to the right and 2 units up or 3 units across (in the x direction) and 2 units up (in the y direction)

• Points in Quadrant 1 have positive x and positive y coordinates. In above figure (4,4) is in first quadrant.
• Points in Quadrant 2 have negative x and positive y coordinates.In above figure (-4,4) is in second quadrant.
• Points in Quadrant 3 have negative x and negative y coordinates. In above figure (-4,-4) is in third quadrant.
  • Points in Quadrant 4 have positive x and negative y coordinates In above figure (4,-4) is in fourth quadrant.