Question

lesson 3 - section 3
understanding rigid transformations and their properties

figures fghu, klmno, and pqrst are transformations of figure abcde. use the graph to answer problems 1 - 4.

1. identify each transformation as a translation, a reflection, or a rotation.
2. draw an arrow on the graph to show the direction of the translation. draw the line of reflection. draw the center and direction of rotation.
3. which angle in each transformation corresponds to ∠e?
4. which side in each transformation corresponds to (overline{ab})?

Explanation:

Step1: Analyze figure FGHIJ

Compare its orientation and position with ABCDE. Since it has a different orientation and can be mapped by flipping, it is a reflection.

Step2: Analyze figure KLMNO

It has the same orientation as ABCDE and is just shifted, so it is a translation.

Step3: Analyze figure PQRST

It has a different orientation and can be rotated to match ABCDE, so it is a rotation.

Step4: For drawing requirements

• For translation (KLMNO), draw an arrow from a corresponding point on ABCDE to the same - point on KLMNO to show direction.
• For reflection (FGHIJ), find the line of symmetry (the perpendicular bisector of corresponding - point segments) and draw it.
• For rotation (PQRST), find the center of rotation (the intersection of perpendicular bisectors of corresponding - point segments) and draw the direction of rotation.

Step5: Find corresponding angle to ∠E

• For FGHIJ, the corresponding angle is ∠J.
• For KLMNO, the corresponding angle is ∠O.
• For PQRST, the corresponding angle is ∠T.

Step6: Find corresponding side to $\overline{AB}$

• For FGHIJ, the corresponding side is $\overline{FG}$.
• For KLMNO, the corresponding side is $\overline{KL}$.
• For PQRST, the corresponding side is $\overline{PQ}$.

Answer:

1. FGHIJ is a reflection, KLMNO is a translation, PQRST is a rotation.
2. Drawings as described above.
3. For FGHIJ: ∠J; for KLMNO: ∠O; for PQRST: ∠T.
4. For FGHIJ: $\overline{FG}$; for KLMNO: $\overline{KL}$; for PQRST: $\overline{PQ}$.