Answer:
![S' = (-5,-5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ul7nm5vvdfs5t0wrwtvxkqih7tiwkr7fvb.png)
![Q](https://img.qammunity.org/2022/formulas/mathematics/high-school/ie7vbc0ak9dlob1i94ngbfvah28c5hgror.png)
Explanation:
Given
![S = (5,-5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yzt7ef5kwyrizze83zwnhezm4csr2gjciv.png)
![Q= (5,5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/qqwfts63shmb1eok6bf4tk5371dh18j9zj.png)
Solving (a): Reflect S across y-axis
The rule to reflect across y-axis is:
![(x,y) \to (-x,y)](https://img.qammunity.org/2022/formulas/mathematics/high-school/8bqq6o7m4fn6b59xtnohgb8e09qc84q8ll.png)
So, we have:
![S(5,-5) \to S'(-5,-5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/xfo62kwmhqduax13ouz4mlfthggwe0bo4x.png)
Hence:
![S' = (-5,-5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ul7nm5vvdfs5t0wrwtvxkqih7tiwkr7fvb.png)
Solving (b): Reflect Q across x and y-axis
The rule to reflect across x-axis is:
![(x,y) \to (x,-y)](https://img.qammunity.org/2022/formulas/mathematics/high-school/cokf5r7ad01buou2wg1wn9q8rjtywes02e.png)
So:
![Q(5,5) \to Q'(5,-5)](https://img.qammunity.org/2022/formulas/mathematics/high-school/f19we8e7bdjq3maunfskk7qgvn33pjwxlw.png)
The rule to reflect across y-axis is:
![(x,y) \to (-x,y)](https://img.qammunity.org/2022/formulas/mathematics/high-school/8bqq6o7m4fn6b59xtnohgb8e09qc84q8ll.png)
So:
![Q'(5,-5) \to Q](https://img.qammunity.org/2022/formulas/mathematics/high-school/u2i6edpsoz618f5hw13eym6rn78ksnbnue.png)
Hence:
![Q](https://img.qammunity.org/2022/formulas/mathematics/high-school/ie7vbc0ak9dlob1i94ngbfvah28c5hgror.png)