An ordered pair is a set of numbers separated by a coma “ , “ and enclosed in parenthesis “ ( ) “. It is represented as (x, y). Here x represents the horizontal distance from the origin and y represents the vertical distance from the origin in the co-ordinate plane.
Example 1: The co-ordinates (1, 7) and (-3, P) are on a straight line x – y = Q. Find the values of P and Q.
Given, Equation of a straight line is x – y = Q.
Two co-ordinates (1, 7) and (-3, P) are on this straight line.
Substitute (1, 7) in the above equation x – y = Q and find the value of Q.
x – y = Q
1 – 7 = Q
-6 = Q
So the straight line equation is x – y = - 6
The second point (-3, P) also lies on the straight line. So, substituting (-3, P) in x – y = -6
-3 – y = -6
Add + 3 on both sides
-3 - P + 3 = - 6 + 3
-P = -3
P = 3
Example 2: Observe the co-ordinates and name the quadrant to which it belongs to.
(a) (-5, 10) (b) (12, 12) (c) ( 8, -9) (d) (-2, -3)
There are four quadrants in the co-ordinate plane. Depending upon the signs of x and y co-ordinates the ordered pair is placed in one of the quadrants.
(a) (-5, 10)
Here x co-ordinate is negative -5 and y co-ordinate is positive 10. Hence it is in the second quadrant.
(b) (12, 12)
Here both x and y coordinates are positive 12. Hence it is in the first quadrant.
(c) (8, - 9)
Here x co-ordinate is positive 8 and y co-ordinate is negative -9. Hence it is in the fourth quadrant.
(d) (-2, -3)
Here x coordinate is negative -2 and y coordinate is also negative -3. Hence this ordered pair is in the third quadrant