Question

the graph shows parallelograms wxyz and wxyz. which sequence of transformations maps wxyz onto wxyz? a translation left 10 units and down 1 unit followed by a rotation 90° counterclockwise around the origin a rotation 90° clockwise around the origin followed by a reflection across the y - axis a reflection across the x - axis followed by a translation left 11 units and up 3

Explanation:

Step1: Analyze translation

Translation rules: For a point $(x,y)$, a translation left $a$ units and down $b$ units gives $(x - a,y - b)$. A rotation $90^{\circ}$ counter - clockwise around the origin transforms a point $(x,y)$ to $(-y,x)$. If we first translate left 10 units and down 1 unit and then rotate $90^{\circ}$ counter - clockwise, the resulting transformation does not match the given parallelograms.

Step2: Analyze rotation and reflection

The rule for a $90^{\circ}$ clockwise rotation around the origin is $(x,y)\to(y, - x)$. The rule for a reflection across the $y$ - axis is $(x,y)\to(-x,y)$. Let's take a vertex of parallelogram $WXYZ$, say $W(9,6)$. A $90^{\circ}$ clockwise rotation gives $(6,-9)$. A reflection across the $y$ - axis gives $(-6,-9)$. By checking all vertices, this sequence of transformations maps $WXYZ$ onto $W'X'Y'Z'$.

Step3: Analyze reflection and translation

The rule for a reflection across the $x$ - axis is $(x,y)\to(x,-y)$. A translation left $a$ units and up $b$ units gives $(x - a,y + b)$. This sequence of transformations does not map $WXYZ$ onto $W'X'Y'Z'$.

Answer:

a rotation $90^{\circ}$ clockwise around the origin followed by a reflection across the $y$-axis