Question

1. does the transformation preserve distance? select yes or no.

transformation
yes
no
rotation about (2, 3)
reflection across line ( y = x )
dilation by factor 0.5

Explanation:

Step1: Recall properties of rotation

Rotation is a rigid transformation. Rigid transformations preserve distance. So rotation about \((2,3)\) preserves distance.

Step2: Recall properties of reflection

Reflection is a rigid transformation. Rigid transformations preserve distance. So reflection across \(y = x\) preserves distance.

Step3: Recall properties of dilation

Dilation changes the size of a figure. If the scale factor \(k
eq1\), the distance between points changes. For a dilation with factor \(0.5\), \(k = 0.5
eq1\), so it does not preserve distance.

Answer:

• Rotation about \((2,3)\): Yes
• Reflection across line \(y = x\): Yes
• Dilation by factor \(0.5\): No