we know that
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
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
step 1
Move the center of the circle 1 onto the
center of the circle 2
the transformation has the following rule
(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
The circles are now concentric (they have the
same center)
step 2
A dilation is needed to decrease the size of
circle 1 to coincide with circle 2
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
A
translation, followed by a dilation will map one circle onto the other,
thus proving that the circles are similar
the answers are
a) The circles are similar because you can translate circle 1 using the translation rule
(x,y)--------> (x-4,y-10)
b) And the dilate it using a scale factor of 0.5
We can translate circle 1 using the translation rule (x-4, y-10) and dilate it using a scale factor of 0.5.
It is given that
Center of circle 1 ≡ (5,8)
Radius of circle 1 = 8cm
Center of circle 2 = (1,-2)
Radius of circle 2 = 4 cm
Difference between x-coordinates of circles = 5-1 = 4
Difference between y-coordinates of circles = 8-(-2) = 10
So, the translation rule will be (x-4, y-10)
A scale factor is a number that multiplies (“scales”) a quantity.
Radius of circle 2 / radius of circle 1 = 2/4 =0.5
Therefore, we can translate circle 1 using the translation rule (x-4, y-10) and dilate it using a scale factor of 0.5.
To get more about dilation visit:
https://brainly.com/question/10253650
