Question

Find the area of a rhombus if its vertices are (3,0), (4, 5).X-1, 4) and (-2, -1) taken in
order. (Hint: Area of a rhombus = 1/2(product of its diagonals)]​

Answer 1

Answer:

24 sq. Units. Expalanation is in the image.

Hope this helps

Answer 2

Answer:

Step-by-step explanation:

firstly finding value of x,

diagonals of a rhombus bisect each other

thus  using midpoint formula,

$(\frac{(x-1)+3}{2} )=(\frac{4 +(-2)}{2} )$

solving this we get x =0

thus our coordinates are

A= (3,0)

B= (4,5)

C= (-1,4)

D= (-2,-1)

now finding the lengths of the diagonals

AC=$\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2}}$

AC= $\sqrt{(3-(-1))^{2}+ (0-4)^{2} }$

AC=4$\sqrt{2}$ units

similarly BD = 6$\sqrt{2}$ units

area =1/2 AC* BD

area = 1/2 * 6*4* 2                          [$(\sqrt{2})^{2}=2$]

area =24 sq. unit