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hammer [34]
2 years ago
6

The four vertices of a rectangle drawn on a complex plane are defined by 1 + 4i, -2 + 4i, -2 – 3i, and 1 – 3i. The area of the r

ectangle is square units.
Mathematics
2 answers:
kompoz [17]2 years ago
7 0
The rectangle is 1-(-2) = 3 units in the real direction and 4i-(-3i) = 7 units in the imaginary direction. Its area is 3×7 = 21 square units.
Anna35 [415]2 years ago
5 0

Answer:

The area of rectangle =21 sq units .

Step-by-step explanation:

Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.

Consider ABCD is  a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.

First we find sides of rectangle

AB=vertices of B- vertices of A

AB= -2+4i-(1+4i)=-3

<h3>If complex number=a+bi</h3><h3>Then modulus=\sqrt{a^2+b^2}</h3><h3>Length of AB= \sqrt{(-3)^2}=3 ( Because magnitude = length always positive ) </h3>

BC= Vertices of C - vertices of B

BC=-2-3i-(-2+4i)=-7i

Length of BC=\sqrt{(-7)^2}=7 ( Magnitude always positive)

CD= vertices of D- vertices of C

CD= 1-3i-(-2-3i)=3

Length of CD= \sqrt{3^2}=3 ( Magnitude  always positive)

DA= vertices of A - vertices of D

DA= 1+4i-(1-3i) =7i

Length of DA= \sqrt{7^2}=7 ( Magnitude always positive)

AB=CD and DA= BC

Length BC=7 units

Breadth AB=3 units

Area of the rectangle = length\times breadth

Area of rectangle =AB\times BC

<h3>Area of rectangle= 3\times 7=21 sq units .</h3>
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An ounce unit will best represent each scenario.

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2 years ago
If the perimeter of the regular decagon shown above is 136 1/4 inches, what is the length of each side?
victus00 [196]
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Ideally you should always post the diagram to help us see the entire problem; however, the diagram is not needed in this case because we are told the figure is regular decagon. So there are 10 sides and each side is the same length. If each side is x inches long, then the perimeter is 10x inches.

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