Question

which transformation, when performed on a geometric figure abc,d, will result in the transformed figure being similar but not congruent to the original figure? a. rotation 270 clockwise b. translation 3 units down c. reflection over y - axis d. dilation with factor 3

Explanation:

• Rotation: A \(270^{\circ}\) clock - wise rotation (Option A) is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the rotated figure is congruent to the original figure.
• Translation: A translation of 3 units down (Option B) is also a rigid transformation. It just moves the figure without changing its shape or size. So, the translated figure is congruent to the original figure.
• Reflection: A reflection over the \(y\) - axis (Option C) is a rigid transformation. It flips the figure over the \(y\) - axis but keeps the shape and size intact. So, the reflected figure is congruent to the original figure.
• Dilation: A dilation with a factor of 3 (Option D) is a non - rigid transformation. If the scale factor \(k

eq1\), the dilated figure has the same shape (so it is similar) but a different size (so it is not congruent) as the original figure.

Answer:

D. Dilation with factor 3