Question

triangles efh and wsy are shown on the coordinate grid where △efh is the pre - image. 6. describe the feature of △wsy that indicates that more than one rigid motion was applied to △efh. 7. draw △efh, the result of the first transformation that was applied to △efh. 8. map the transformation of one vertex of △efh to △wsy. 9. complete the table. transformation mapping algebraic description △efh→△efh △efh→△wsy 10. explain how you know if the sequence of transformations preserves distance.

Explanation:

Step1: Analyze orientation change

The orientation of $\triangle WSY$ is different from $\triangle EFH$. A single - rigid motion like translation only moves the figure without changing its orientation. Since the orientation is changed, more than one rigid motion was likely applied.

Step2: Assume first transformation (example)

Let's assume the first transformation is a rotation. If we rotate $\triangle EFH$ about a point, we can get $\triangle E'F'H'$. To draw it, we need to determine the center of rotation, angle of rotation. For simplicity, assume a 90 - degree counter - clockwise rotation about the origin (if applicable based on the grid). Each point $(x,y)$ of $\triangle EFH$ is transformed to $(-y,x)$.

Step3: Map a vertex transformation

Let's take vertex $E$ of $\triangle EFH$. After the first rotation to get $E'$ in $\triangle E'F'H'$, then to map $E'$ to the corresponding vertex in $\triangle WSY$, we may need a translation. If $E=(x_1,y_1)$ becomes $E'=(x_2,y_2)$ after rotation and then $E'$ needs to be translated $a$ units in the $x$ - direction and $b$ units in the $y$ - direction to get to the corresponding vertex in $\triangle WSY$. The mapping for the translation is $(x,y)\to(x + a,y + b)$.

Step4: Complete the table (example)

For $\triangle EFH\to\triangle E'F'H'$, if it's a 90 - degree counter - clockwise rotation about the origin, the mapping is $(x,y)\to(-y,x)$ and the algebraic description is a rotation transformation. For $\triangle E'F'H'\to\triangle WSY$, if it's a translation $a$ units right and $b$ units up, the mapping is $(x,y)\to(x + a,y + b)$ and the algebraic description is a translation transformation.

Step5: Explain distance - preservation

Rigid motions (rotations, translations, reflections) preserve distance. Since each step in the sequence of transformations is a rigid motion, the overall sequence preserves distance. The distance between any two points in $\triangle EFH$ is the same as the distance between the corresponding two points in $\triangle WSY$ because rotations and translations do not change the lengths of line - segments.

Answer:

1. The change in orientation of $\triangle WSY$ compared to $\triangle EFH$ indicates more than one rigid motion.
2. (Draw $\triangle E'F'H'$ based on assumed rotation as described above).
3. (Describe vertex - mapping as described above).

9.

Transformation	Mapping	Algebraic Description
Translation (assumed second)	$(x,y)\to(x + a,y + b)$	Translation transformation

1. Since each transformation in the sequence is a rigid motion (rotations and translations), the sequence preserves distance as rigid motions do not change the lengths of line - segments.