Question

Circle 1 is centered at (−4, −2)(−4, −2) and has a radius of 3 centimeters. Circle 2 is centered at (5, 3)(5, 3) and has a radius of 6 centimeters. 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 delete it using a scale factor of .

Answer 1

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