Question

which sequence of transformations produces an image that is not congruent to the original figure?
a. a translation of 5 units to the left followed by a dilation of a factor of 2
b. a translation of 3 units to the left followed by a reflection across the x - axis
c. a rotation of 90° clockwise followed by a translation of 6 units to the left
d. a reflection across the y - axis followed by a rotation of 180° counterclockwise

Explanation:

• Translation: A translation (sliding) of a figure does not change its size or shape.
• Reflection: A reflection (flipping) of a figure does not change its size or shape.
• Rotation: A rotation (turning) of a figure does not change its size or shape. These three transformations (translation, reflection, rotation) are called rigid transformations and produce congruent images.
• Dilation: A dilation (scaling) changes the size of a figure. If the scale factor is not \(1\), the image is not congruent to the original figure.

Answer:

A. A translation of 5 units to the left followed by a dilation of a factor of 2