To determine which statement is true regarding the dilation of a triangle by a scale factor of \(\pi=\frac{1}{3}\), we first need to understand how the scale factor affects the dimension of the triangle.
In general, dilation is a transformation that alters the size of a figure by a specified factor, known as the scale factor, without changing its shape. The scale factor \(\pi\), which is given as \(\pi = \frac{1}{3}\), falls within the interval from \(0\) to \(1\).
When a scale factor is:
- Greater than \(1\) (i.e., \(n>1\)), the figure undergoes enlargement, making the image larger than the original.
- Between \(0\) and \(1\) (i.e., \(0- Negative or zero, it generally has no typical geometric meaning in standard dilation and is not considered here.
Given the scale factor \(\pi = \frac{1}{3}\), it lies between \(0\) and \(1\) (\(0<\frac{1}{3}<1\)). This means that the triangle is being reduced in size.
Thus, the correct statement is:
- It is a reduction because \(0
So the true statement regarding the dilation of the triangle by a scale factor of \(\pi = \frac{1}{3}\) is:
"It is a reduction because [tex]\(0
