Answer:
![k(x,y) --> k'(x,y-7)](https://img.qammunity.org/2021/formulas/mathematics/college/wglj6x7kmd3zobb99yl764avewqvabjswf.png)
Explanation:
Given
![k = (-3,4)](https://img.qammunity.org/2021/formulas/mathematics/college/zn2tq3l56sd5qyg0pwm4qmo096ealaunwt.png)
Translation: 7 units down
Required
Determine the rule to produce k'
When an (x,y) coordinate is translated down by h units, the resulting point is:
(x,y) --> (x, y - h)
In this case:
![h = 7](https://img.qammunity.org/2021/formulas/mathematics/college/wlzscis0uxbbx5vlt1t18rog61mkvxwadj.png)
So, we have:
![k(x,y) --> k'(x,y-7)](https://img.qammunity.org/2021/formulas/mathematics/college/wglj6x7kmd3zobb99yl764avewqvabjswf.png)
Hence, option A answers the question.
Solving further to determine the coordinates of k'.
![k = (-3,4)](https://img.qammunity.org/2021/formulas/mathematics/college/zn2tq3l56sd5qyg0pwm4qmo096ealaunwt.png)
![k' = (-3,4-7)](https://img.qammunity.org/2021/formulas/mathematics/college/8gk0zpbx01ahg7q8fwgj8x1j98q1yhxqvb.png)
![k' = (-3,-3)](https://img.qammunity.org/2021/formulas/mathematics/college/88khjgszzzjiateo9ecjmnrd2b4iarfnjn.png)