Question

1. consider the pre - image & image below. what sequence of transformations will map quadrilateral abcd onto quadrilateral abcd?

reflect then rotate 270° clockwise

rotate 90° then a reflection

rotate 90° clockwise then translate to the right

clear all

Explanation:

Step1: Analyze each option

• Option 1: Reflect then rotate \(270^{\circ}\) clockwise
• A reflection changes the orientation of the figure. Then a \(270^{\circ}\) clockwise rotation (equivalent to a \(90^{\circ}\) counter - clockwise rotation) will not map the pre - image \(ABCD\) to the image \(A'B'C'D'\).
• Option 2: Rotate \(90^{\circ}\) then a reflection
• A \(90^{\circ}\) rotation (say counter - clockwise) changes the position of the vertices. Then a reflection (depending on the axis) will not map \(ABCD\) to \(A'B'C'D'\).
• Option 3: Rotate \(90^{\circ}\) clockwise then translate to the right
• When we rotate the rectangle \(ABCD\) \(90^{\circ}\) clockwise around its center (or any fixed point), the orientation of the rectangle changes. Then, by translating (shifting) the rotated rectangle to the right, we can map the pre - image \(ABCD\) to the image \(A'B'C'D'\).

Answer:

Rotate \(90^{\circ}\) clockwise then translate to the right.