Answer:
Whereby circle  P can be obtained from circle
P can be obtained from circle  O by applying the transformations of a translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4,
O by applying the transformations of a translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4,  O is similar to
O is similar to  P
P
Step-by-step explanation:
The given center of the circle  O = (-2, 7)
O = (-2, 7)
The radius of  O, r₁ = 5
O, r₁ = 5
The given center of the circle  P = (12, -1)
P = (12, -1)
The radius of  P, r₂ = 12
P, r₂ = 12
The similarity transformation to prove that  O and
O and  P are similar are;
P are similar are;
a) Move circle  O 14 units to the right and 8 units down to the point (12, -1)
O 14 units to the right and 8 units down to the point (12, -1)
b) Apply a scale of S.F. = r₂/r₁ = 12/5 = 2.4
Therefore, the radius of circle  O is increased by 2.4
O is increased by 2.4
We then obtain  O' with center at (12, -1) and radius r₃ = 2.4×5 = 12 which has the same center and radius as circle
O' with center at (12, -1) and radius r₃ = 2.4×5 = 12 which has the same center and radius as circle  P
P
∴ Circle  P can be obtained from circle
P can be obtained from circle  O by applying similarity transformation of translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4,
O by applying similarity transformation of translation of T₍₁₄, ₋₈₎ followed by a dilation by a scale factor of 2.4,  O is similar to
O is similar to  P.
P.