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3 years ago

Octagon ABCDEFGH and its dilation, octagon A'B'C'D'E'F'G'H', are shown on the coordinate plane below:

Mathematics

2 answers:

Grace [21]3 years ago

7 0

Answer:

the answer would be 2

Step-by-step explanation:

Otrada [13]3 years ago

5 0

From the coordinates given we can make out that dilaton is having a scale factor of 2.

Explanaton:

A = (3,1): A' =(6,2)

B = (3,-1) : B' = (6,-2)

C = (1,-3): C' = (2,-6)

D = (-1,-3): D'=(-2,-6)

E =(-3, -1): E'= (-6,-2)

F = (-3,1): F'=(-6,2)

G = (-1,3) : G' = (-2,6)

H = (1,3): H' = (2,-6)

We find that all the coordinates have become doubled as that of original.

Let us find length of AB :

AB = distance between A and B =2 units

A'B' = distance between A' and B' =4 units

i.e. length increased by a scale factor of 2

Hence dilation with scale factor 2.

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Here a right angled triangle given. one angle with measure $45^o$ given. The three sides of the triangle given 4, x, y.

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We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

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Now we will use SOHCAHTOA that is $sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}$ , where x is the angle given.

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We know the value of $tan(45^o) = 1$ . By substituting the value we will get,

$1 =\frac{4}{x}$

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

$(1)(x) = (\frac{4}{x}) (x)$

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So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

$sin(45^o) =\frac{4}{y}$

we know the value of $sin(45^o) =\frac{\sqrt{2}}{2}$

By substituting the value we will get,

$\frac{\sqrt{2}}{2} = \frac{4}{y}$

By cross multiplying we will get,

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We will get y by dividing both sides by $\sqrt{2}$ , we will get,

$\frac{\sqrt{2}y}{\sqrt{2}} =\frac{8}{\sqrt{2} }$

$y =\frac{8}{\sqrt{2} }$

Now we will rationalize the denominator by multiplying $\sqrt{2}$ to the top and bottom.

$y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}$

$y =\frac{8\sqrt{2}}{2}$

$y = 4\sqrt{2}$

So we have got the required values of x and y.

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3 years ago

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mixer [17]

Answer:

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Step-by-step explanation:

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4 years ago

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