Current Affairs 9th Class

Category : 9th Class

Co-ordinate Geometry

• Co-ordinate Geometry: The branch of mathematics in which geometric problems are solved through algebra by using the coordinate system is known as coordinate geometry.
• In coordinate geometry, every point is represented by an ordered pair, called coordinates of that point.
• A pair of numbers 'a' and V listed in a specific order with 'a' at the first place and 'b' at the second place is called an ordered pair (a, b).

            Note :(i) (a, b) \[\ne \] (b, a)

            (ii) If (a, b) = (c, d) then a = a and b=d.

• The position of a point in a plane is determined with reference to two fixed mutually perpendicular lines called the coordinate axes.

• The horizontal line is called X-axis and the vertical line is called Y-axis.

• The point of intersection of the coordinate axes is called origin 0(0, 0).

• In a point P (a, b), 'a' is called x-coordinate or first coordinate or abscissa and 'b' is called y- coordinate or second coordinate or ordinate.

• The axes divide the plane into four quadrants,

(i) \[{{Q}_{1}}\]is the I quadrant? Here both x and y are positive i.e., x > 0 and y > 0. The ordered pair (a, b) belongs to this quadrant.

            (ii) \[{{Q}_{2}}\]is the II quadrant. Here x is negative and y is positive i.e., x < 0 and y > 0. The ordered pair (-a, b) belongs to this quadrant.

            (iii) \[{{Q}_{3}}\]is the III quadrant. Here both x and y are negative, i.e., x < 0 and y < 0. The ordered pair (-a,- b) belongs to the quadrant,                                                      

            (iv) \[{{Q}_{4}}\]is the IV quadrant. Here x is positive and y is negative i.e., x > 0 and y < 0. The ordered pair (a, -b) belongs to this quadrant.                                               

• The coordinates of any point on X - axis is of the form (a, 0) [y-coordinate zero],

•  The coordinates of any point on Y - axis is of the form (0, b) [x-coordinate zero].