Question

Triangle D has been dilated to create triangle D′. Use the image to answer the question.

image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 18, 24, 30

Determine the scale factor used.

1/2

2

3

1/3

Answer 1

The scale factor is 3

Explanation:

For triangle D to be dilated into triagle D', each side of D is multiplied by 3,i.e,

6 * 3 = 18

8 * 3 = 24

10 * 3 = 30

Therefor, the scale factor to turn triangle D to D' is 3

Answer 2

To determine the scale factor used, we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are 6, 8, and 10.

In triangle D', the corresponding side lengths are 18, 24, and 30.

To find the scale factor, we can divide the corresponding side lengths of triangle D' by the corresponding side lengths of triangle D.

Side length ratio:

18/6 = 3

24/8 = 3

30/10 = 3

The ratio of corresponding side lengths is consistent at 3 for each pair. Therefore, the scale factor used is 3.

So, the correct answer is 3.

Explanation:

Step 1: Identify the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 6, 8, and 10.

In triangle D', the corresponding side lengths are given as 18, 24, and 30.

Step 2: Calculate the ratio of each corresponding side length of D' to D.

For the first pair of corresponding sides:

18/6 = 3

For the second pair of corresponding sides:

24/8 = 3

For the third pair of corresponding sides:

30/10 = 3

Step 3: Analyze the ratios obtained.

Since all three ratios are equal to 3, it indicates a consistent scale factor between the corresponding side lengths of the two triangles.

Step 4: Determine the scale factor.

The scale factor is the constant ratio by which each corresponding side length is multiplied to obtain the corresponding side length of the larger triangle. In this case, since the ratio is 3 for all pairs, the scale factor used is 3.

So, the step-by-step explanation confirms that the scale factor used is 3.