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Dahasolnce [82]
3 years ago
7

Very Confused please help!

Mathematics
1 answer:
Nataly_w [17]3 years ago
4 0
We know that<span>
<span>Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. 
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that</span>
<span> Circle 1 is centered at (5,8) and has a radius of 8 centimeters
 Circle 2 is centered at (1,-2) and has a radius of 4 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule</span>
(x,y)--------> (x-4,y-10)
so
(5,8)------> (5-4,8-10)-----> (1,-2)
so
center circle 1 is now equal to center circle 2 
<span>The circles are now concentric (they have the same center)
</span>
step 2
<span>A dilation is needed to decrease the size of circle 1 to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle 1-----> 4/8----> 0.5

radius circle 1 will be=8*scale factor-----> 8*0.5-----> 4 cm
radius circle 1 is now equal to radius circle 2 

<span>A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

the answer is
</span>
</span>The circles are similar because you can translate Circle 1 using the transformation rule (x-4,y-10) and then dilate it using a scale factor of (0.5)
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