Question

which of the following always changes when a figure is dilated (scale ≠ 1)?
shape
angle measures
orientation
size
question 3
triangle def is dilated by a factor of 1/3. what happens to its side lengths?
each side is one - third as long
each side is the same
side lengths change but not proportionally

Explanation:

Step1: Recall properties of dilation

Dilation is a transformation that changes the size of a figure. When a figure is dilated with a scale factor \(k
eq1\), the shape remains the same (similar figures), angle measures remain the same (similarity preserves angles), and orientation remains the same. But the size (lengths of sides) changes. For a dilation with scale factor \(k\), the length of each side of the new figure is \(k\) times the length of the corresponding side of the original figure.

Step2: Analyze triangle dilation

For triangle \(DEF\) dilated by a scale factor of \(\frac{1}{3}\). If the original side length is \(s\), the new side length \(s'\) is given by the formula \(s'=\frac{1}{3}s\). This means each side is one - third as long.

Answer:

For the first question: Size.
For the second question: Each side is one - third as long.