Question

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

The circles are similar because you can translate Circle 1 using the transformation rule ( __ _, ___) and then dilate it using a scale factor of ____
.

Answer 1

Circle 1 is centered at (5, 8) and has a radius of 8 cm

Circle 2 is centered at (1, −2) and has a radius of 4 cm

To transform circle 1 to circle 2 ⇒⇒ we need to transform (5,8) to (1,-2)
the transformation rule (x-4 , y-10)
because 5-1 = 4 and 8-(-2) = 10

while circle 1 has a radius = 8 and the circle 2 has a radius = 4 cm

So, the dilation factor = 4/8 = 0.5


The correct answer is :

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