Question

which sequence of transformations maps wxyz onto wxyz? a rotation 90° clockwise around the origin followed by a reflection across the y - axis a rotation 90° clockwise around the origin followed by a translation right 8 units a rotation 90° counterclockwise around the origin followed by a translation up 6 units

Explanation:

Step1: Recall rotation rules

A 90 - degree clockwise rotation around the origin $(x,y)\to(y, - x)$. A 90 - degree counter - clockwise rotation around the origin $(x,y)\to(-y,x)$.

Step2: Analyze first transformation

Let's assume a point $(x,y)$ in $WXYZ$. For a 90 - degree clockwise rotation around the origin, its image is $(y,-x)$.

Step3: Analyze second transformation options

If we consider the reflection across the $y$ - axis, $(y,-x)\to(-y,-x)$. If we consider the translation right 8 units, $(y,-x)\to(y + 8,-x)$. If we consider the 90 - degree counter - clockwise rotation followed by translation up 6 units, first $(x,y)\to(-y,x)$ and then $(-y,x)\to(-y,x + 6)$.
Let's take a vertex of $WXYZ$, say $W(-5,-2)$.

• For a 90 - degree clockwise rotation around the origin: $W(-5,-2)\to W_1(-2,5)$.
• Reflection across the $y$ - axis: $W_1(-2,5)\to W_2(2,5)$ (This is not correct).
• Translation right 8 units: $W_1(-2,5)\to W_3(6,5)$ (This is correct).
• For a 90 - degree counter - clockwise rotation, $W(-5,-2)\to W_4(2,-5)$ and translation up 6 units gives $W_5(2,1)$ (This is not correct).

Answer:

a rotation 90° clockwise around the origin followed by a translation right 8 units