Question

question 19 (5 points) circles c and c are similar. state the translation rule and the scale factor of dilation. a) to obtain c, circle c is translated to the left three units and up two units and is dilated with a scale factor of 1/2. b) to obtain c, circle c is translated to the right three units and down two units and is dilated with a scale factor of one. c) to obtain c, circle c is translated to the right four units and down three units and is dilated with a scale factor of one. d) to obtain c, circle c is translated to the right three units and down two units and is dilated with a scale factor of two.

Explanation:

Step1: Identify circle centers

Let center of $C$ be $(1,0)$, center of $C'$ be $(-2,2)$.

Step2: Calculate translation rule

$\Delta x = -2 - 1 = -3$, $\Delta y = 2 - 0 = 2$. So translate left 3, up 2.

Step3: Find radii and scale factor

Radius of $C$ is 2, radius of $C'$ is 1. Scale factor: $\frac{1}{2}$.

Step4: Match with options

This matches option A.

Answer:

A) To obtain C', circle C is translated to the left three units and up two units and is dilated with a scale factor of $1/2$.