IX-MATHS: CO-ORDINATE GEOMETRY

CO-ORDINATE GEOMETRY

In coordinate geometry, points are placed on the "coordinate plane" .  It has two scales - one running across the plane called the     "x axis" and another a right angles to it called the y axis. (The point where the axes cross is called the origin and is where both x and y are zero.

On the x-axis, values to the right are positive and those to the left are negative.
On the y-axis, values above the origin are positive and those below are negative.

A point's location on the plane is given by two numbers,the first tells where it is on the x-axis and the second which tells where it is on the y-axis. Together, they define a single, unique position on the plane. So in the diagram above, the point A has an x value of 20 and a y value of 15. These are the coordinates of the point A, sometimes referred to as its "rectangular coordinates". Note that the order is important; the x coordinate is always the first one of the pair.

The co-ordinates of a point are of the form
 ( + , + ) in the first quadrant, 
 (-, + ) in the second quadrant,
 ( - , - ) in the third quadrant and
 ( + , -) in the fourth quadrant,
where + denotes a positive real number and – denotes a negative real number.

Any point in  I quadrant = (x,y)
Any point in  II quadrant =  (- x, y)
Any point in III quadrant = ( -x , -y)
Any point in IV quadrant = ( x , -y )
Any point in X-axis = ( x,0)or (-x , 0)
Any point in Y axis = ( 0, y )or ( 0, -y)

Exercise (3.1):Question(1) : 
How will you describe the position of a table lamp on your study table to another person?

Solution:

Consider that the lamp is placed on the table. Choose two adjacent edges, DC and AD. Then, draw perpendiculars on the edges DC and AD from the position of lamp and measure the lengths of these perpendiculars. Let the length of these perpendiculars be 30 cm and 20 cm respectively. Now, the position of the lamp from the left edge (AD) is 20 cm and from the lower edge (DC) is 30 cm. This can also be written as (20, 30), where 20 represents the perpendicular distance of the lamp from edge AD and 30 represents the perpendicular distance of the lamp from edge DC.

Exercise -3.1: Question No.(2): Refer the question from the text book.

Solution: 

Both the cross-streets are marked in the above figure. It can be observed that there is only one cross-street which can be referred as (4, 3), and again, only one street which can be referred as (3, 4).

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