Center of circle 1 = (-4,-2)
Center of circle 2 = (5,3)
From -4 to 5 is a 9 unit move to the right.
From -2 to 3 is a 5 unit move up.
You would need to add 9 to the x value and 5 to the y value.
The transformation rule would be (x+9, y+5)
The radius of circle 2 is twice the length of circle 1, so to make the radius of circle 1 the same as circle 2 multiple it by 2, this is the scale factor.
Scale factor = 2
The transformation for Circle 1 is (x+9) , (y + 5) and Scale factor of Circle 1 is 2 .
Scale is defined as the ratio of the length of any object on a model (blueprint) to the actual length of the same object in the real world.
The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left.
According to the question
Circle 1
Centre : (−4, −2)
Radius : 3 centimeters
Circle 2
Centre : (5, 3)
Radius : 6 centimeters
Transformations can be applied to Circle 1 to prove that the circles are similar
As Circle 2 and Circle 1 do not have same coordinates
so ,
Circle 1 have to use transformation rules
difference between coordinates of Circle 2 and Circle 1 is
x2 - x1 = 5 - (-4 ) = 9
y2 - y1 = 3 - (-2) = 5
Therefore,
transformation for Circle 1 : (x+9) , (y + 5)
now,
Scale factor between Circle 2 and Circle 1 is :
As Radius of Circle 2 = 2 * Radius of Circle 1
Therefore,
Scale factor of Circle 1 = 2
Hence, the transformation for Circle 1 is (x+9) , (y + 5) and Scale factor of Circle 1 is 2 .
To know more about transformation and Scale factor here:
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