Question

how does a dilation affect the angles of a figure?
a. the angles change based on the scale factor.
b. the angles double in size.
c. the angles halve in size.
d. the angles remain the same.
what role does translation play in proving that all circles are similar?
a. scales the radius of one circle to match another
b. reflects one circle onto another
c. aligns the centers of two circles after dilation
d. rotates one circle to overlap another
two circles have radii 4 and 12, with centers at (1,1) and (-2,5). what transformations are needed to make the smaller circle similar to the larger circle?
a. dilation reflection
b. dilation and translation
c. reflection and translation
d. translation and rotation

Explanation:

Step1: Recall dilation property

Dilation is a transformation that changes the size of a figure but not its shape. Angles are preserved under dilation as it only affects the lengths of the sides of the figure proportionally. So, the angles remain the same.

Step2: Recall translation in circle - similarity

Translation moves a figure without changing its size, shape, or orientation. To prove all circles are similar, first, we can use dilation to change the radius of one circle to match another. Then, translation is used to align the centers of the two circles.

Step3: Analyze circle - transformation

For two circles with different radii and different - centered positions, we first use dilation to change the radius of the smaller circle to match the larger one. Then, we use translation to move the center of the smaller - radius circle to the center of the larger - radius circle.

Answer:

1. d. The angles remain the same.
2. c. Aligns the centers of two circles after dilation
3. b. Dilation and translation