Practice Solutions

1. Reflect over the x-axis

$$\begin{gathered} \left(3, 2\right)\to \left(3, –2\right) \\ \left(5, 5\right)\to \left(5, –5\right) \\ \left(6, 1\right)\to \left(6, –1\right) \end{gathered}$$

2. Reflect over the y-axis

$$\begin{gathered} \left(3, 2\right)\to \left(–3, 2\right) \\ \left(5, 5\right)\to \left(–5, 5\right) \\ \left(6, 1\right)\to \left(–6, 1\right) \end{gathered}$$

3. Reflect over the y-axis.

$$\begin{gathered} \left(–6, –1\right)\to \left(6, –1\right) \\ \left(–7, –5\right)\to \left(7, –5\right) \\ \left(–1, –4\right)\to \left(1, –4\right) \\ \left(0, 0\right)\to \left(0, 0\right) \end{gathered}$$

4. Reflect over the x-axis.

$$\begin{gathered} \left(–6, –1\right)\to \left(–6, 1\right) \\ \left(–7, –5\right)\to \left(–7, 5\right) \\ \left(–1, –4\right)\to \left(–1, 4\right) \\ \left(0, 0\right)\to \left(0, 0\right) \end{gathered}$$

5. Translate the figure three units right and five units up.

$$\begin{gathered} \left(–1, 1\right)\to \left(–1+3, 1+5\right)\to \left(2, 6\right) \\ \left(–1, –3\right)\to \left(–1+3, –3+5\right)\to \left(2, 2\right) \\ \left(4, –1\right)\to \left(4+3, –1+5\right)\to \left(7, 4\right) \\ \left(2, 2\right)\to \left(2+3, 2+5\right)\to \left(5, 7\right) \end{gathered}$$

6. Translate the figure two units left and six units up.

$$\begin{gathered} \left(–1, –4\right)\to \left(–1–2, –4+6\right)\to \left(–3, 2\right) \\ \left(–5, 0\right)\to \left(–5–2, 0+6\right)\to \left(–7, 6\right) \\ \left(1, 1\right)\to \left(1–2, 1+6\right)\to \left(–1, 7\right) \end{gathered}$$

7. Translate the figure six units left and three units down.

$$\begin{gathered} \left(2, 0\right)\to \left(2–6, 0–3\right)\to \left(–4, –3\right) \\ \left(6, 4\right)\to \left(6–6, 4–3\right)\to \left(0, 1\right) \\ \left(–3, 5\right)\to \left(–3–6, 5–3\right)\to \left(–9, 2\right) \end{gathered}$$

8. Translate the figure four units right and four units up.

$$\begin{gathered} \left(–2, 4\right)\to \left(–2+4, 4+4\right)\to \left(2, 8\right) \\ \left(3, 4\right)\to \left(3+4, 4+4\right)\to \left(7, 8\right) \\ \left(3, 2\right) \to \left(3+4, 2+4\right)\to \left(7, 6\right) \\ \left(–2, 2\right)\to \left(–2+4, 2+4\right)\to \left(2, 6\right) \end{gathered}$$