Write the coordinates of the vertices after a rotation of 180 degrees counterclock wise around the origin.

Mathematics

1 answer:

Kryger [21]3 years ago

3 0

A 180° rotation just means to switch the signs of x and y and then swap them.

So if you have (3,5) it would become (-5,-3)

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What is the value of x in the diagram below?

Furkat [3]

Hi,
The answer will be $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = $\frac{adjacent side}{hypotenuse}$ so, if we applied this rule on the lower triangle we can say: cos30°= $\frac{9}{hypotenuse}$ and therefore the hypotenuse = $\frac{9}{cos30}$ = $\frac{18}{ \sqrt{3} }$ .

now in the upper triangle we will apply the same rule so,
cos45°= $\frac{adjacent side}{hypotenuse}$
and the adjacent side in the upper triangle is $\frac{18}{ \sqrt{3} }$ and the hypotenuse is x.
so cos45°= $\frac{( \frac{18}{ \sqrt{3} } )}{x}$ and then we can say
x= $\frac{ \frac{18}{ \sqrt{3} } }{cos45}$ = $\frac{ 18\sqrt{2} }{ \sqrt{3} }$ .

4 0

3 years ago

Read 2 more answers

The polygon in the diagram is a regular octagon with center A. Find the area of the octagon to the nearest tenth of a foot. A) 2

IRISSAK [1]

Method 1: In order to find out the area of an octagon with a radius of 4 feet, we have to split the whole figure into 8 equal isosceles triangles.
Therefore,
We will find out the area of one triangle and multiply the area with 8 to, figure out the area of the whole octagon there are 8 similar triangles and all of them will have the same area.

Method 2: From method 1, it would take time as there are too much of calculation, therefore we would go for the shortcut using the formula:

Area = 2√2 × r²

where r<span> is the radius of the octagon.
Substituting the values,
We get:
</span>Area = 2√2 × 4²
Area = 2√2 × 16
Area = 2× 1.41 × 16
Area = 2.828 × 16
Area = 45.25

Rounded to the nearest tenth:

Area = 45.3 ft²