Question

1. determine what transformations occurred and in what order:

xyz is first

to ( xyz ), then

to ( xyz ),
and finally

to ( xyz ).

1. describe the transformation for ( xyz \to xyz ).
2. describe the transformation for ( xyz \to xyz ).
3. describe the transformation for ( xyz \to xyz ).
4. write the algebraic description for the sequence of transformations from 7 - 9:

Explanation:

Step1: Analyze \( XYZ\to X'Y'Z'\)

• Translation: A translation moves a figure without rotating or resizing.
• Reflection: A reflection flips a figure over a line.
• Rotation: A rotation turns a figure around a point.
• Dilation: A dilation resizes a figure.
• By observing the coordinates, \( XYZ\) to \( X'Y'Z'\) is a rotation.

Step2: Analyze \( X'Y'Z'\to X''Y''Z''\)

• \( X'Y'Z'\) to \( X''Y''Z''\) is a reflection.

Step3: Analyze \( X''Y''Z''\to X'''Y'''Z'''\)

• \( X''Y''Z''\) to \( X'''Y'''Z'''\) is a translation.

Answer:

1. \( XYZ\) is first rotated to \( X'Y'Z'\), then reflected to \( X''Y''Z''\), and finally translated to \( X'''Y'''Z'''\).
2. Rotation.
3. Reflection.
4. Translation.

10.

Transformation	Algebraic Description
\( X'Y'Z'\to X''Y''Z''\)	\((x,y)\to\) (reflection formula, e.g., if reflected over \( x\) - axis \((x,y)\to(x, - y)\))
\( X''Y''Z''\to X'''Y'''Z'''\)	\((x,y)\to(x + a,y + b)\) (where \( a,b\) are translation amounts)