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3 years ago

Describe the rule for the rotation.

Mathematics

1 answer:

finlep [7]3 years ago

4 0

Answer:

Step-by-step explanation:

If you draw a line from the origin (0,0) to L ( the original point ) and a different line from the origin to the image L' you can see the angle of rotation as being

90 degrees and that the rotation is clockwise.

the rule is (x, y) become ( y, -x)

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Please help i am stuck and trying not to fail lol. also if you can show work pls

wel

Given:

The figure of rectangle.

To find:

a. The diagonal of the rectangle.

b. The area of the rectangle.

c. perimeter of the rectangle.

Solution:

(a)

In a right angle triangle,

$\sin \theta=\dfrac{Perpendicular}{Hypotenuse}$

$\sin 30=\dfrac{12}{Hypotenuse}$

$\dfrac{1}{2}=\dfrac{12}{Hypotenuse}$

$Hypotenuse=12\times 2$

$Hypotenuse=24$

So, the diagonal of the of the rectangle is 24 units.

(b)

In a right angle triangle,

$\tan \theta=\dfrac{Perpendicular}{Base}$

$\tan 30=\dfrac{12}{Base}$

$\dfrac{1}{\sqrt{3}}=\dfrac{12}{Base}$

$Base=12\sqrt{3}$

Length of the rectangle is 12 and width of the rectangle is $12\sqrt{3}$ . So, the area of the rectangle is:

$Area=length \times width$

$Area=12 \times 12\sqrt{3}$

$Area=144\sqrt{3}$

So, the area of the rectangle is $144\sqrt{3}$ sq. units.

(c)

Perimeter of the rectangle is:

$P=2(length+width)$

$P=2(12+12\sqrt{3})$

$P=24+24\sqrt{3}$

$P\approx 65.57$

Therefore, the perimeter of the rectangle is about 65.57 units.

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