Question

the graph shows triangles klm and klm. which sequence of transformations maps klm onto klm? a rotation 90° clockwise around the origin followed by a translation right 1 unit and up 1 unit. a reflection across the y - axis followed by a translation right 11 units and down 10 units. a rotation 180° around the origin followed by a translation right 9 units and down 1 unit.

Explanation:

Step1: Analyze rotation effect

A 90 - degree clockwise rotation around the origin has a specific rule for coordinate transformation $(x,y)\to(y, - x)$. But this doesn't seem to match the transformation from $\triangle KLM$ to $\triangle K'L'M'$.

Step2: Analyze reflection effect

A reflection across the $y$-axis changes the sign of the $x$-coordinate of each point $(x,y)\to(-x,y)$. After reflection across the $y$-axis, then a translation right 11 units and down 10 units can map $\triangle KLM$ to $\triangle K'L'M'$.

Step3: Analyze 180 - degree rotation

A 180 - degree rotation around the origin changes the signs of both coordinates $(x,y)\to(-x,-y)$. This doesn't match the transformation from $\triangle KLM$ to $\triangle K'L'M'$.

Answer:

a reflection across the $y$-axis followed by a translation right 11 units and down 10 units