Question
If a scale factor of 1/3 is applied to a triangle the new image will be
Answers
GPT-4o mini
When a scale factor of \( \frac{1}{3} \) is applied to a triangle, the dimensions of the triangle will be reduced to one-third of their original size. This means:
1. Each side length of the triangle will be multiplied by \( \frac{1}{3} \).
2. The area of the triangle will be affected as well. The area will be reduced by the square of the scale factor. Therefore, the new area will be \( \left(\frac{1}{3}\right)^2 = \frac{1}{9} \) of the original area.
In summary, the new triangle will be similar to the original triangle (same shape, different size) with side lengths that are one-third of the original and an area that is one-ninth of the original area.
1. Each side length of the triangle will be multiplied by \( \frac{1}{3} \).
2. The area of the triangle will be affected as well. The area will be reduced by the square of the scale factor. Therefore, the new area will be \( \left(\frac{1}{3}\right)^2 = \frac{1}{9} \) of the original area.
In summary, the new triangle will be similar to the original triangle (same shape, different size) with side lengths that are one-third of the original and an area that is one-ninth of the original area.