Points and are chosen on the coordinate plane under the following conditions: • The…

MATHEMATICS · Multi-part · CBSE · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Points

P

and

Q

are chosen on the coordinate plane under the following conditions: • The abscissa of

P

is a negative integer greater than

-7

, and its ordinate is a positive integer less than

6

. • The abscissa of

Q

equals the ordinate of

P

. • The ordinate of

Q

is the negative of the abscissa of

P

. (i) Write

P

(a,b)

and express the given numerical conditions on

a

and

b

using inequalities. (ii) Express the coordinates of

Q

in terms of

a

and

b

. (iii) Using the inequalities from part (i), list every possible ordered pair for

P

, and for each such

P

write the corresponding coordinates of

Q

. (iv) For every pair

(P,Q)

obtained in part (iii), state the quadrant in which

P

lies and the quadrant in which

Q

lies. Describe any pattern you observe and justify it using the signs of the coordinates.