Question

A triangle is dilated using a scale factor of 3. The image is then dilated using a scale factor of 1/2. What scale factor can you use to dilate the original triangle to obtain the final image?

A) 1.5
B) 2
C) 3
D) 6

Answer 1

To find the equivalent single scale factor for two consecutive dilations of a triangle, multiply the scale factors together. For a triangle dilated by a scale factor of 3 and then 1/2, the resulting single scale factor is 1.5.

Step-by-step explanation:

The question is asking How to obtain the final image of a triangle after a series of dilations with given scale factors. Initially, a triangle is dilated by a scale factor of 3 and then by a scale factor of ½. To find the single scale factor that could replace these two successive dilations, we can multiply the two given scale factors together:

Scale factor of first dilation = 3

Scale factor of second dilation = 1/2

Combined scale factor = 3 × 1/2 = 3/2 = 1.5

Therefore, starting with the original triangle, by applying a scale factor of 1.5, you can achieve the same result as the two-stage dilation process.