Question

Circle P is dilated by a scale factor of 1.5 to create circle P'. The area of circle P is x square units.

What is the area in square units of circle P'?
Responses
A 1.5x square units1.5 x square units
B (1.5x)2 square units(1.5 x ) 2 square units
C 1.52x square units1.5 2 x square units
D 2(1.5 + x) square units

Answer 1

The area of a circle is proportional to the square of its radius. Since the radius of circle P' is 1.5 times the radius of circle P (due to the dilation factor of 1.5), the area of circle P' will be 1.5^2 times the area of circle P.

Therefore, the area of circle P' is (1.5^2)(x) square units.

Simplifying, this becomes 2.25x square units.

The correct answer is C.