Question

circle a has a radius of 8 inches. it then undergoes a dilation with a scale factor of 5/4, resulting in circle b. next, circle b undergoes a dilation with a scale factor of 1/2, resulting in circle c. finally, circle c undergoes a dilation with a scale factor of 8/5, resulting in circle d. what is the overall scale factor between the radius of circle a and circle d?
o 5/4
o 1/8
o 8
o 1

Explanation:

Step1: Multiply the scale - factors

The scale factors are $\frac{5}{4}$, $\frac{1}{2}$, and $\frac{8}{5}$. Multiply them together: $\frac{5}{4}\times\frac{1}{2}\times\frac{8}{5}$.

Step2: Simplify the product

First, multiply the numerators together: $5\times1\times8 = 40$. Then multiply the denominators together: $4\times2\times5=40$. So, $\frac{5\times1\times8}{4\times2\times5}=\frac{40}{40}=1$.

Answer:

1