Question

Polygon 1 has an area of square feet. Polygon 1 is dilated by a scale factor of 4 using the origin as the center of dilation to create Polygon 2. What is the area in square feet of Polygon 2? A 144�144r144r square feet B 2.25�2.25r2.25r square feet C 576�576r576r square feet D 36�36r36r square feet

Answer 1

The area of Polygon 2, which is dilated by a scale factor of 4, would be 16 times the area of Polygon 1. Since we denote the area of Polygon 1 as 'r', the area of Polygon 2 is 16r (16 times r). The correct answer is 576r square feet.

Step-by-step explanation:

When a polygon is dilated by a scale factor, the area of the polygon is affected by the square of the scale factor.

In this problem, Polygon 1 is dilated by a scale factor of 4 to create Polygon 2, which means that each dimension of Polygon 1 is multiplied by 4.

Thus, the area of Polygon 2 will be the area of Polygon 1 multiplied by the scale factor squared (42 = 16).

We are not given the specific area of Polygon 1, but we can denote it as 'r'.

Hence, the area of Polygon 2 will be 16r square feet. If the area of Polygon 1 is r, the area of Polygon 2, when using a scale factor of 4, will be 16r.

The correct answer to the problem is: C. 576r square feet, since the area of the original polygon has been multiplied by the square of the scale factor, which is 42 = 16, and hence the area is 16 times larger.