Question
The length of a side of a triangle is 10 inches before a dilation. After the dilation, the length of the new side is 6. What scale factor was used?
Answers
GPT-4o mini
To find the scale factor used in the dilation, you can use the formula for the scale factor (k):
\[
k = \frac{\text{length after dilation}}{\text{length before dilation}}
\]
In this case, the length before dilation is 10 inches and the length after dilation is 6 inches. Plugging in the values:
\[
k = \frac{6}{10}
\]
This simplifies to:
\[
k = \frac{3}{5}
\]
Therefore, the scale factor used in the dilation is \(\frac{3}{5}\).
\[
k = \frac{\text{length after dilation}}{\text{length before dilation}}
\]
In this case, the length before dilation is 10 inches and the length after dilation is 6 inches. Plugging in the values:
\[
k = \frac{6}{10}
\]
This simplifies to:
\[
k = \frac{3}{5}
\]
Therefore, the scale factor used in the dilation is \(\frac{3}{5}\).