Circle 1 is centered at (6, 8) and has a radius of 8 units. Circle 2 is centered at (6, −3)

and has a radius of 2 units.

What transformations can be applied to Circle 1 to prove that the circles are similar?

Enter your answers in the boxes.
The circles are similar because you can translate Circle 1 using the transformation rule ( _ , _ ) and then dilate it using a scale factor of _

Question

03-04-2018
Mathematics

contestada

Circle 1 is centered at (6, 8) and has a radius of 8 units. Circle 2 is centered at (6, −3)

and has a radius of 2 units.

What transformations can be applied to Circle 1 to prove that the circles are similar?

Enter your answers in the boxes.
The circles are similar because you can translate Circle 1 using the transformation rule ( _ , _ ) and then dilate it using a scale factor of _

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calculista calculista · Answer 1 · 2018-04-14T01:03:08+02:00

we know that

the equation of a circle is(x-h)²+(y-k)²=r²

for the circle 1---------> (x-6)²+(y-8)²=8²
for the circle 2---------> (x-6)²+(y+3)²=2²

using a graph tool
see the attached figure

What transformations can be applied to Circle 1 to prove that the circles are similar?

we know that
r2/r1---------> 2/8------> 1/4
to prove that the circle 1 and circle 2 are similar, the radius of circle 1 must be multiplied by (1/4) and translate the center of the circle 1 (11) units down

the answer is
The circles are similar because you can translate Circle 1 using the transformation rule
(x,y)--------------> ( x , y-11 )
and then
dilate it using a scale factor of (1/4)