Question

1. two circles have diameters of 8 and 24, and their centers are 5 units apart. what transformations are needed to map the smaller circle onto the larger circle? a. rotation and dilation b. dilation and translation c. reflection and dilation d. translation and reflection

Explanation:

Step1: Analyze dilation need

The diameters of the two circles are 8 and 24. The ratio of the diameters is $\frac{24}{8}=3$, so a dilation with a scale - factor of 3 is needed to change the size of the smaller circle to match the larger one.

Step2: Analyze translation need

The centers of the circles are 5 units apart. A translation is needed to move the center of the dilated - smaller circle to the center of the larger circle. There is no need for rotation or reflection.

Answer:

B. Dilation and translation