Question

question 15 (multiple choice worth 1 points) (02.01r, 2.02r mc) which transformation or sequence of transformations would produce an image that is not congruent to its pre - image? a translation followed by a reflection a rotation of 90 degrees about the origin a dilation followed by a rotation a translation of (x + 3, y + 4)

Explanation:

• Translation followed by a reflection: Both translation (sliding) and reflection (flipping) are rigid transformations. Rigid transformations preserve the shape and size of the figure, so the image is congruent to the pre - image.
• Rotation of 90 degrees about the origin: Rotation is a rigid transformation. It changes the orientation of the figure but not its shape and size. So the image is congruent to the pre - image.
• Dilation followed by a rotation: Dilation changes the size of the figure (if the scale factor is not 1). Rotation is a rigid transformation (preserves shape and size). Since dilation can change the size (e.g., if scale factor \(k

eq1\)), the image is not congruent to the pre - image.

• Translation of \((x + 3,y + 4)\): Translation is a rigid transformation. It just moves the figure in the coordinate plane without changing its shape and size. So the image is congruent to the pre - image.

Answer:

C. A dilation followed by a rotation