Question

Find the area of a rhombus if its vertices are (3,0), (4,5), (-1,4), &(-2,-1) taken in order.​

Answer 1

Answer:

Step-by-step explanation:

Let A(3,0),B(4,5), C(−1,4) and D(−2,−1) are the vertices of rhombus ABCD.

AC and BD are the diagonals of rhombus.

∴BD=  

(x  

1

​  

−x  

2

​  

)  

2

+(y  

1

​  

−y  

2

​  

)  

2

 

​  

 

Here x  

1

​  

=4,x  

2

​  

=−2 and y  

1

​  

=5,y  

2

​  

=−1

⇒BD=  

(4−(−2))  

2

+(5−(−1))  

2

 

​  

 

⇒BD=  

6  

2

+6  

2

 

​  

=  

36+36

​  

=  

72

​  

=6  

2

​  

 

∴AC=  

(x  

1

​  

−x  

2

​  

)  

2

+(y  

1

​  

−y  

2

​  

)  

2

 

​  

 

Here x  

1

​  

=3,x  

2

​  

=−1 and y  

1

​  

=0,y  

2

​  

=4

⇒BD=  

(3−(−1))  

2

+(0−4)  

2

 

​  

 

⇒BD=  

4  

2

+(−4)  

2

 

​  

=  

16+16

​  

=  

32

​  

=4  

2

​  

 

Area of rhombus =  

2

1

​  

×Product of diagonals

=  

2

1

​  

×6  

2

​  

×4  

2

​  

 

=  

2

24×2

​  

=24 Sq.uni

Answer 2

Answer:

hope it helps........