Question

reasoning abcd is a rectangle. given abcd ≅ abcd, describe two rigid motions that map abcd to abcd. use pencil and paper. describe a way to show abcd is identical to abcd. choose the correct answer below. a. translation 6 units left, reflection across the x - axis b. translation 4 units down, rotation of 90° about the origin c. reflection across the x - axis, translation 4 units up d. reflection across the y - axis, translation 4 units down

Explanation:

To determine the correct rigid motions mapping \(ABCD\) to \(A'B'C'D'\), we analyze each option:

• Option A: Translating 6 units left and reflecting over the \(x\)-axis would not align the rectangles.
• Option B: Translating 4 units down and rotating \(90^\circ\) about the origin changes the shape’s orientation incorrectly.
• Option C: Reflecting over the \(x\)-axis (flips vertically) and translating 4 units up aligns \(ABCD\) with \(A'B'C'D'\) (since \(A'B'C'D'\) is above \(ABCD\) after reflection).
• Option D: Reflecting over the \(y\)-axis and translating 4 units down misaligns the rectangles.

Answer:

C. Reflection across the x - axis, translation 4 units up