Question

tell whether the transformation appears to be a rigid motion. explain. 1. preimage image 2. preimage image show the reflection of △abc across line ℓ. 3. 4.

Explanation:

Step1: Recall definition of rigid - motion

A rigid motion preserves side - lengths and angle - measures.

Step2: Analyze problem 1

The pre - image and image of the pentagon have the same shape and size. All side - lengths and angle - measures are preserved. So, it is a rigid motion.

Step3: Analyze problem 2

The pre - image has an extra rectangular part that is not in the image. Side - lengths and angle - measures are not preserved. So, it is not a rigid motion.

Step4: For problems 3 and 4 (showing reflection)

To show the reflection of $\triangle ABC$ across line $\ell$:

1. For each vertex (e.g., $A$, $B$, $C$), draw a perpendicular line from the vertex to line $\ell$.
2. Measure the distance from the vertex to line $\ell$ along the perpendicular.
3. On the other side of line $\ell$, mark a point at the same distance from line $\ell$ along the perpendicular. This new point is the image of the original vertex.
4. Connect the new points to form the reflected triangle.

Answer:

1. Yes, it is a rigid motion because side - lengths and angle - measures are preserved.
2. No, it is not a rigid motion because side - lengths and angle - measures are not preserved.
3. Follow the steps above to show the reflection of $\triangle ABC$ across line $\ell$.
4. Follow the steps above to show the reflection of $\triangle ABC$ across line $\ell$.