Question

which sequence of transformations maps rst onto rst? a translation right 3 units and up 10 units followed by a reflection across y - axis a reflection across the x - axis followed by a rotation 90° clockwise around origin a rotation 180° around the origin followed by a translation left 3 units and 4 units

Explanation:

Step1: Analyze option 1

Translation right 3 units and up 10 units: $(x,y)\to(x + 3,y+10)$. Then reflection across y - axis: $(x,y)\to(-x,y)$. This will not map $\triangle RST$ to $\triangle R'S'T'$.

Step2: Analyze option 2

Reflection across x - axis: $(x,y)\to(x,-y)$. Then rotation 90° clockwise around origin: $(x,y)\to(y,-x)$. Let's assume a point $(x,y)$ on $\triangle RST$. After reflection across x - axis we get $(x,-y)$, and after 90° clockwise rotation we get $(-y,-x)$. This sequence of transformations will map $\triangle RST$ to $\triangle R'S'T'$.

Step3: Analyze option 3

Rotation 180° around origin: $(x,y)\to(-x,-y)$. Then translation left 3 units and down 4 units: $(x,y)\to(x - 3,y - 4)$. This will not map $\triangle RST$ to $\triangle R'S'T'$.

Answer:

A reflection across the x - axis followed by a rotation 90° clockwise around origin.