Question

question 1 1 pts

triangle 1 is dilated by a scale factor of 4.1 using the origin as the center of dilation to create triangle 2. which statement about the area and perimeter of triangle 2 is true?

the perimeter is 4.1 times the perimeter of triangle 1, and the area is 4.1 times the area of triangle 1.

the perimeter is 8.2 times the perimeter of triangle 1, and the area is 8.2 times the area of triangle 1.

the perimeter is 4.1 times the perimeter of triangle 1, and the area is 16.81 times the area of triangle 1.

the perimeter is 16.4 times the perimeter of triangle 1, and the area is 16.81 times the area of triangle 1.

Explanation:

Step1: Perimeter relationship

When a figure is dilated by a scale factor \(k\), the perimeter of the new figure is \(k\) times the perimeter of the original figure. Here, \(k = 4.1\), so the perimeter of Triangle 2 is \(4.1\) times the perimeter of Triangle 1.

Step2: Area relationship

When a figure is dilated by a scale factor \(k\), the area of the new figure is \(k^{2}\) times the area of the original figure. Since \(k = 4.1\), then \(k^{2}=4.1\times4.1 = 16.81\), so the area of Triangle 2 is \(16.81\) times the area of Triangle 1.

Answer:

The perimeter is 4.1 times the perimeter of Triangle 1, and the area is 16.81 times the area of Triangle 1.