Question

Prove that the four points (2, 6), (5, 1), (0, - 2) and (- 3, 3) are the vertices
of a square; find the area of the square formed.

Answer 1

Answer:

Let A(0-1), B(6,7), C(-2,3) and D(8,3) be the given points. Then

,AD=  

(8−0)  

2

+(3+1)  

2

 

​  

=  

64+16

​  

=4  

5

​  

 

BC=  

(6+2)  

2

+(7−3)  

2

 

​  

=  

64+16

​  

=4  

5

​  

 

AC=  

(−2−0)  

2

+(3+1)  

2

 

​  

=  

4+16

​  

=2  

5

​  

 

and,

BD=  

(8−6)  

2

+(3−7)  

2

 

​  

=  

4+6

​  

=2  

5

​  

 

∴AD=BCandAC=BD

So, ADBC is a parallelogram

Now

AB=  

(6−0)  

2

+(7+1)  

2

 

​  

=  

36+64

​  

=10

and,CD=  

(8+2)  

2

+(3−3)  

2

 

​  

=10

Clearly,AB  

2

=AD  

2

+DB  

2

andCD  

2

=CB  

2

+BD  

2

 

Hence, ADBC is a rectangle.

Now

,Area of rectangle ADBC=AD×DB=(4  

5

​  

×2  

5

​  

)sq. units=40sq. units

Step-by-step explanation: