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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)

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

(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