Question

which sequence of transformations maps opqr onto opqr? a reflection across the line y = x followed by a translation left 4 units and down 6 units a rotation 90° clockwise around the origin followed by a reflection across the line y = -3 a translation left 6 units and down 9 units followed by a rotation 90° counterclockwise around the origin

Explanation:

Step1: Analyze reflection across $y = x$

The rule for reflecting a point $(x,y)$ across the line $y = x$ is $(y,x)$. But this doesn't match the orientation of the transformation from $OPQR$ to $O'P'Q'R'$.

Step2: Analyze 90 - degree clock - wise rotation

The rule for rotating a point $(x,y)$ 90 - degree clock - wise around the origin is $(y, - x)$. After rotation, reflecting across $y=-3$ doesn't match the transformation.

Step3: Analyze translation and rotation

Let's assume a point $(x,y)$ in $OPQR$. First, a translation left 6 units and down 9 units gives $(x - 6,y - 9)$. Then a 90 - degree counter - clockwise rotation around the origin (rule: $(x,y)\to(-y,x)$) matches the transformation from $OPQR$ to $O'P'Q'R'$.

Answer:

a translation left 6 units and down 9 units followed by a rotation 90° counterclockwise around the origin