Question

show that the points A (3,5) B(6,0) C(1,-3) and D(-2,2)are the vertices of the square ABCD​

Answer 1

Answer:

A(x

1 ,y

1 )=(3,5)

B(x 2 ,y 2 )=(6,0)

C(x 3y 3 )=(1,−3)

D(x

4

,y

4

)=(−2,2)

Then,

Distance between

AB=

(x

1

−x

2

)

2

+(y

1

−y

2

)

2

=

(3−6)

2

+(5−0)

2

=

9+25

AB=

34

BC=

(x

2

−x

3

)

2

+(y

2

−y

3

)

2

=

(6−1)

2

+(0+3)

2

=

25+9

BC=

34

CD=

(x

3

−x

4

)

2

+(y

3

−y

4

)

2

=

(1+2)

2

+(−3−2)

2

=

9+25

CD=

34

DA=

(x

4

−x

1

)

2

+(y

4

−y

1

)

2

=

(−2−3)

2

+(2−5)

2

=

25+9

DA=

34

Then, AB=BC=CD=DA

All sides are equal.

Hence, ABCD is a square