Mathematics

Problem

Consider four positions on a treasure map, each described in words: (i) Point

P

2

units left of the

y

-axis and

3

units above the

x

-axis. (ii) Point

Q

5

units right of the

y

-axis and

3

units above the

x

-axis. (iii) Point

R

5

units right of the

y

-axis and

4

units below the

x

-axis. (iv) Point

S

2

units left of the

y

-axis and

4

units below the

x

-axis. Answer the following: (a) Write the coordinates of the points

P,\,Q,\,R

and

S

. (b) Without using any distance formula, state whether

PQR S

forms a rectangle. Give reasons referring only to equal abscissae or equal ordinates wherever required. (c) Write the name of the quadrant (or axis) in which each point lies.

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