Help me please ...................

Mathematics

1 answer:

Feliz [49]3 years ago

4 0

Answer:

can you elabrate on that please

Step-by-step explanation:

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The coordinates of rhombus ABCD are A(–4, –2), B(–2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nea

anyanavicka [17]

Hello !
If you mist find the area of the rhombus,you need to calculate the length of the diagonals.

We have the rhombus ABCD.The diagonals are are AC and BD .
<span>Here's a formula to find out the distance between two points in the Cartesian system : (let's take randomly 2 point and their coordinates)
</span>
<span> M (m₁,m₂) ; N (n₁,n₂) ⇒ MN = \sqrt{ (m_{1} - n_{1})^{2} + (m_{2} - n_{2})^{2} }
</span>

Now it's simple to calculate the diagonals :

$AC = \sqrt{ (-4-6)^{2} +(-2-8)^{2}} \\ \\ AC= \sqrt{ (-10)^{2} + (-10)^{2} } \\\\AC = \sqrt{ 100+100} \\\\ AC =\sqrt{ 200 } \\\\AC=10 \sqrt{2} \\ \\ \\ BD = \sqrt{ (-2-4)^{2} + 6^{2} } \\\\BD=\sqrt{ (-6)^{2} + 6^{2} }\\\\BD= \sqrt{6^{2}+6^{2}} \\\\BD= \sqrt{36+36} \\\\BD= \sqrt{72} \\\\BD=6 \sqrt{2}$

The area is : $\frac{AC*BD}{2} = \frac{ 10\sqrt{2} * 6\sqrt{2} }{2} = \frac{60*2}{2} =60$

Answer: 60 u²

The representation is below.
Have a nice day :)