Question

understanding rigid transformations and their properties
figures fghij, 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 transformation of FGHIJ

By observing orientation and position changes, FGHIJ is a translation of ABCDE as it is just shifted without flipping or rotating.

Step2: Analyze transformation of KLMNO

KLMNO is a reflection of ABCDE as it is flipped across a line (to be drawn in next - step).

Step3: Analyze transformation of PQRST

PQRST is a rotation of ABCDE as it is turned around a point (to be determined in next - step).

Step4: Draw for translation

For the translation of FGHIJ, draw an arrow from a corresponding point on ABCDE to the same - named point on FGHIJ to show the direction of movement.

Step5: Draw for reflection

For the reflection of KLMNO, find the line of symmetry between ABCDE and KLMNO and draw it.

Step6: Draw for rotation

For the rotation of PQRST, find the center of rotation (the point around which it is rotated) and draw an arc with an arrow to show the direction of rotation.

Step7: Find corresponding angle for ∠E

In FGHIJ, the corresponding angle to ∠E is ∠J; in KLMNO, it is ∠O; in PQRST, it is ∠T.

Step8: Find corresponding side for $\overline{AB}$

In FGHIJ, the corresponding side to $\overline{AB}$ is $\overline{FG}$; in KLMNO, it is $\overline{KL}$; in PQRST, it is $\overline{PQ}$.

Answer:

1. FGHIJ: Translation; KLMNO: Reflection; PQRST: Rotation
2. Draw arrow for translation of FGHIJ, line of reflection for KLMNO, center and direction of rotation for PQRST (on the graph).
3. FGHIJ: ∠J; KLMNO: ∠O; PQRST: ∠T
4. FGHIJ: $\overline{FG}$; KLMNO: $\overline{KL}$; PQRST: $\overline{PQ}$