Math's: Coordinate System: Coordinate of a Point and Quadrants

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Coordinate System

Coordinate System is a method that identifies the position of a point in a plane by using two perpendicular number lines or axes represented as and .

Coordinate System

Coordinate System

  • The horizontal number line is called x-axis and the vertical number line is called y-axis. The point , where both axes intersect each other is called the origin.

  • The positive direction of x-axis is taken to the right of the origin , and the negative direction is taken to the left of the origin , i.e., the side .

  • Similarly, the portion of y-axis above the origin , i.e., the side is taken as positive and the portion below the origin , i.e., the side is taken as negative.

Coordinate of a Point

The position of a point is given by two numbers, called co-ordinates which refer to the distances of the point from these two axes. The first number, the -co-ordinate (or abscissa), indicates the distance from the -axis (in units) and the second number, the -coordinate (or ordinate) indicates the distance from the -axis (in units).

Coordinate of a Point

Coordinate of a Point

  • The co-ordinates of the origin are .

  • The co-ordinate or ordinate of every point on the -axis is .

  • The co-ordinate or abscissa of every point on the -axis is

In the adjacent figure, the co-ordinates of the points and are and respectively.

1. Write the abscissa and ordinate of the following points

(i)

(ii)

(iii)

Sol- (i) Abscissa- ; Ordinate-

(ii) Abscissa- ; Ordinate-

(iii) Abscissa- ; Ordinate-

Quadrants

The two axes and divide the plane into four parts called quadrants. The four quadrants are named as follows:

four quadrants

Four Quadrants

  • : I Quadrant.

  • : II Quadrant.

  • : III Quadrant.

  • : IV Quadrant.

  • Co-ordinates of all points in the first quadrant are of the type .

  • Any point in the II quadrant has x co-ordinate negative and y co-ordinate positive .

  • Similarly, in III quadrant, a point has both x and y co-ordinates negative .

  • In IV quadrant, a point has x co-ordinate positive and y co-ordinate negative .

2. State the quadrant of each of the following points

(i)

(ii)

(iii)

(iv)

Sol- (i) II Quadrant

(ii) IV Quadrant

(iii) I Quadrant

(iv) III Quadrant

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