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postnew [5]
2 years ago
14

22. the blue figure is a dilation image of the black figure. The center of the dilation is O. Tell whether the dilation is am en

largement or a reduction. Then find the scale factor

Mathematics
2 answers:
emmainna [20.7K]2 years ago
8 0
Since I can't view the image you attached, I'll just provide you a guide for solving the scale factor:


To find<span> a </span>scale factor<span> between two similar figures,</span>find<span> two corresponding sides and write the ratio of the two sides. If you begin with the smaller </span>figure, yourscale factor<span> will be less than one. If you begin with the larger </span>figure<span>, your </span>scale factor<span> will be greater than one.</span>
Troyanec [42]2 years ago
5 0

Answer:

In the figure we can see that the dilation is an enlargement from the black figure to the blue figure.

The factor would be found by taking two points and dividing them. For example, at the right side we have that the point was from x=2 to x=4, their division would be 4/2=2. Now, we take the point in the left side x=-1 and x=-2, if we divide them we have -2/-1=2.

Therefore, the scale factor is 2.

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Please answer asap!!!!!
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Step-by-step explanation:

The equation of a circle can be the expanded form of

\large \text{$(x-a)^2+(y-b)^2=r^2$}(x−a)

2

+(y−b)

2

=r

2

where rr is the radius of the circle, (a,\ b)(a, b) is the center of the circle, and (x,\ y)(x, y) is a point on the circle.

Here, the equation of the circle is,

\begin{gathered}\begin{aligned}&x^2+y^2+10x-4y-20&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4-49&=&\ \ 0\\ \\ \Longrightarrow\ \ &x^2+y^2+10x-4y+25+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &x^2+10x+25+y^2-4y+4&=&\ \ 49\\ \\ \Longrightarrow\ \ &(x+5)^2+(y-2)^2&=&\ \ 7^2\end{aligned}\end{gathered}

⟹

⟹

⟹

⟹

x

2

+y

2

+10x−4y−20

x

2

+y

2

+10x−4y+25+4−49

x

2

+y

2

+10x−4y+25+4

x

2

+10x+25+y

2

−4y+4

(x+5)

2

+(y−2)

2

=

=

=

=

=

0

0

49

49

7

2

From this, we get two things:

\begin{gathered}\begin{aligned}1.&\ \ \textsf{Center of the circle is $(-5,\ 2)$.}\\ \\ 2.&\ \ \textsf{Radius of the circle is $\bold{7}$ units. }\end{aligned}\end{gathered}

1.

2.

Center of the circle is (−5, 2).

Radius of the circle is 7 units.

Hence the radius is 7 units.

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