Question

which sequence of transformations maps klm onto klm? a rotation 180° around the origin followed by a translation right 9 units and down 1 unit 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

Explanation:

Step1: Recall rotation rules

A 180 - degree rotation around the origin changes the sign of both coordinates of a point $(x,y)$ to $(-x,-y)$. A 90 - degree clockwise rotation around the origin changes a point $(x,y)$ to $(y, - x)$. A reflection across the y - axis changes a point $(x,y)$ to $(-x,y)$.

Step2: Analyze the first option

For a 180 - degree rotation around the origin of a point $(x,y)$ we get $(-x,-y)$. Then a translation right 9 units and down 1 unit changes $(-x,-y)$ to $(-x + 9,-y-1)$.

Step3: Analyze the second option

For a 90 - degree clockwise rotation around the origin of a point $(x,y)$ we get $(y,-x)$. Then a translation right 1 unit and up 1 unit changes $(y,-x)$ to $(y + 1,-x + 1)$.

Step4: Analyze the third option

For a reflection across the y - axis of a point $(x,y)$ we get $(-x,y)$. Then a translation right 11 units and down 10 units changes $(-x,y)$ to $(-x+11,y - 10)$.

Step5: Check the coordinates of the points

Let's assume some coordinates for the vertices of $\triangle KLM$ and apply the transformations. If we consider the general rules of rotation and translation, a 180 - degree rotation around the origin followed by a translation right 9 units and down 1 unit will map $\triangle KLM$ onto $\triangle K'L'M'$.

Answer:

a rotation 180° around the origin followed by a translation right 9 units and down 1 unit