Question

select the correct answer.
which sequence of transformations performed on shape i confirms the congruence of shape ii and shape i?
a. a reflection across the y-axis and then a translation 2 units left
b. a 90° counterclockwise rotation about the origin and then a translation 4 units up
c. a 90° clockwise rotation about the origin and then a translation 14 units up and 18 units left
d. a 180° rotation about the origin and then a translation 18 units up and 2 units left

Explanation:

To determine the correct transformation sequence, we analyze each option:

• Option A: A reflection over the \( y \)-axis and then a translation 2 units left. This does not align with the orientation and position change between the two shapes.
• Option B: A \( 90^\circ \) counterclockwise rotation and then a translation 4 units up. The rotation direction and translation distance do not match the transformation from Shape I to Shape II.
• Option C: A \( 90^\circ \) clockwise rotation about the origin and then a translation 14 units up and 18 units left. The rotation and translation distances do not fit.
• Option D: A \( 180^\circ \) rotation about the origin (which flips the shape both horizontally and vertically) and then a translation 18 units up and 2 units left. This sequence correctly transforms Shape I to match the orientation and position of Shape II.

Answer:

D. a \( 180^\circ \) rotation about the origin and then a translation 18 units up and 2 units left