Question

which sequences of transformations map klm onto klm? select all that apply. a translation right 1 unit and up 4 units followed by a rotation 90° clockwise around the origin a reflection across the x - axis followed by a rotation 180° around the origin a rotation 90° clockwise around the origin followed by a translation right 4 units and down 1 unit a rotation 180° around the origin followed by a translation right 1 unit and up 8 units

Explanation:

Step1: Recall transformation rules

Translation moves a figure, rotation turns it around a point.

Step2: Analyze option 1

Translation right 1 unit and up 4 units: $(x,y)\to(x + 1,y + 4)$. Then 90 - degree clock - wise rotation around origin: $(x,y)\to(y,-x)$. This does not map $\triangle KLM$ to $\triangle K'L'M'$.

Step3: Analyze option 2

Reflection across x - axis: $(x,y)\to(x,-y)$. Then 180 - degree rotation around origin: $(x,y)\to(-x,-y)$. This does not map $\triangle KLM$ to $\triangle K'L'M'$.

Step4: Analyze option 3

90 - degree clock - wise rotation around origin: $(x,y)\to(y,-x)$. Then translation right 4 units and down 1 unit: $(x,y)\to(x + 4,y-1)$. This maps $\triangle KLM$ to $\triangle K'L'M'$.

Step5: Analyze option 4

180 - degree rotation around origin: $(x,y)\to(-x,-y)$. Then translation right 1 unit and up 8 units: $(x,y)\to(x + 1,y + 8)$. This does not map $\triangle KLM$ to $\triangle K'L'M'$.

Answer:

a rotation 90° clockwise around the origin followed by a translation right 4 units and down 1 unit