Rectangle ABCD with four 90 degree angles, undergoes and translation followed by a dilation. Which of the following properties are NOT preserved after this composition transformation?

Question

a. orientation
b. distance
c. shape
d. angle measure

Answer 1

To determine which properties are NOT preserved after the composition of a translation followed by a dilation, let's analyze each transformation:

1. Translation: Translations shift all points of a figure a certain distance in a specified direction. This transformation preserves:

   • Orientation
   • Distances (between points)
   • Shape (the figure remains the same shape)
   • Angle measures (angles remain the same)

2. Dilation: Dilation changes the size of the figure while keeping the shape the same (the proportions are preserved). This transformation preserves:

   • Shape (the figure remains similar to the original)
   • Angle measures (angles remain the same)
   • However, it does not preserve distances (since distances between points change according to the scale factor).

Now, when you compose these transformations (translation followed by dilation), the overall properties you are left with are as follows:

• Orientation: Preserved during translation, but the effect of dilation doesn’t change the orientation of the figure.
• Distance: NOT preserved, as dilation does alter distances.
• Shape: Preserved, as both transformations keep the shape (the rectangle remains a rectangle).
• Angle measure: Preserved, angles remain the same throughout both transformations.

Thus, the property that is NOT preserved after the composition of a translation followed by a dilation is:

b. distance