Answer:
Translate circle V (x+9, y+8)
Dilate circle V by a scale factor of 4
Step-by-step explanation:
To prove that two circles are similar:
- Center the smaller circle on the larger circle so that the two circles share a center point.
- Identify the scale factor of dilation needed to increase the smaller circle to the size of the larger circle by dividing the radius of the larger circle by that of the smaller circle.
From inspection of the given diagram:
- Center of Circle V = (-8, -6)
- Center of Circle V' = (1, 2)
Therefore, to translate Circle V to Circle V', shift Circle V 9 units right and 8 units up → (x+9, y+8).
From inspection of the given diagram
- Radius of Circle V = 2 units
- Radius of Circle V' = 8 units
Therefore, the scale factor of dilation is:
[tex]\sf \implies scale\:factor=\dfrac{8}{2}=4[/tex]
Since we have used translation and dilation to map Circle V to Circle V', we can conclude that Circle V and Circle V' are similar.
