Question

9. Draw a square with vertices:
P(-2,2);Q(2,2);R(2,-2);S(-2,-2).​

Answer 1

Answer:

ANSWER

PQ=

(3−2)

2

+(4+1)

2

=

1+25

=

26

units

QR=

(−2−3)

2

+(3−4)

2

=

25+1

=

26

units

RS=

(−3+2)

2

+(−2−3)

2

=

1+25

=

26

units

PS=

(−3−2)

2

+(−2+1)

2

=

25+1

=

26

units

PR=

(−2−2)

2

+(3+1)

2

=

16+16

=

32

=4

2

units

QS=

(−3−3)

2

+(−2−4)

2

=

36+36

=

72

=6

2

units

Now we can see that,

PQ=QR=RS=PS=

26

units but PR



=QS

⇒PQRS is a quadrilateral whose all sides are equal but diagonals are not equal.

⇒PQRS is a rhombus, not a square.

∴ Area of rhombus PQRS =

2

1

× (Product of diagonals)

⇒

2

1

×PR×QS =

2

1

×4

2

×6

2

=24 sq.units