Question

the rule $t_{1, - 4}circ r_{o,180^{circ}}(x,y)$ is applied to rectangle klmn. which rectangle shows the final image? o 1 o 2 o 3 o 4

Explanation:

Step1: Analyze the rotation rule

The rule $R_{O,180^{\circ}}(x,y)=(-x,-y)$. This rotates a point $(x,y)$ 180 - degrees about the origin.

Step2: Analyze the translation rule

The rule $T_{1,-4}(x,y)=(x + 1,y-4)$. After rotation, we apply this translation.

Step3: Apply the rules to rectangle KLMN

First, rotate each vertex of rectangle KLMN 180 - degrees about the origin using $R_{O,180^{\circ}}$. Then, translate the rotated vertices using $T_{1,-4}$.

Answer:

(Without seeing the specific details of rectangles 1 - 4, we can't give a specific option. But the above are the steps to find the final - image rectangle.)