Question

A sequence of transformations is described below.

A dilation about a point P
A rotation about another point Q
A vertical stretch about the horizontal line PQ
A reflection over a line PQ
Option 1: Dilation → Rotation → Vertical Stretch → Reflection
Option 2: Rotation → Vertical Stretch → Reflection → Dilation
Option 3: Vertical Stretch → Reflection → Dilation → Rotation
Option 4: Reflection → Dilation → Rotation → Vertical Stretch

Answer 1

The correct sequence of transformations is Reflection → Dilation → Rotation → Vertical Stretch.

Step-by-step explanation:

The correct sequence of transformations is Option 4: Reflection → Dilation → Rotation → Vertical Stretch.

First, we perform a reflection over the line PQ. This will flip the figure across the line.

Next, we perform a dilation about point P. This will either enlarge or shrink the figure.

Then, we perform a rotation about point Q. This will rotate the figure around the point.

Finally, we perform a vertical stretch about the horizontal line PQ. This will stretch or compress the figure vertically.