Question

1. plot points (11, 11) (16, 16) (16, 6). label this figure #21.
2. translate #21 down 22 units. label this figure #22.
3. reflect #22 across the y axis. label this figure #23.
4. translate #23 up 22 units. label this figure #24.
5. rotate #24 90° clockwise. label this figure #25.
6. rotate #25 180° clockwise. label this figure #26.
7. reflect #26 across the y axis. label this figure #27.
8. rotate #27 180° clockwise. label this figure #28.

Explanation:

First, correct the errors in the prior steps (22 and 23) to establish accurate starting points:

Step1: Fix Step22 (translate down 22)

For a point $(x,y)$, translate down 22: $(x, y-22)$

• $(11,11) \to (11, 11-22)=(11,-11)$
• $(16,16) \to (16, 16-22)=(16,-6)$
• $(16,6) \to (16, 6-22)=(16,-16)$

Step2: Fix Step23 (reflect over y-axis)

For a point $(x,y)$, reflect over y-axis: $(-x,y)$

• $(11,-11) \to (-11,-11)$
• $(16,-6) \to (-16,-6)$
• $(16,-16) \to (-16,-16)$

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Step3: Step24 (translate up 22)

For a point $(x,y)$, translate up 22: $(x, y+22)$

• $(-11,-11) \to (-11, -11+22)=(-11,11)$
• $(-16,-6) \to (-16, -6+22)=(-16,16)$
• $(-16,-16) \to (-16, -16+22)=(-16,6)$

Step4: Step25 (rotate 90° clockwise)

For a point $(x,y)$, rotate 90° clockwise: $(y,-x)$

• $(-11,11) \to (11,11)$
• $(-16,16) \to (16,16)$
• $(-16,6) \to (6,16)$

Step5: Step26 (rotate 180° clockwise)

For a point $(x,y)$, rotate 180° clockwise: $(-x,-y)$

• $(11,11) \to (-11,-11)$
• $(16,16) \to (-16,-16)$
• $(6,16) \to (-6,-16)$

Step6: Step27 (reflect over y-axis)

For a point $(x,y)$, reflect over y-axis: $(-x,y)$

• $(-11,-11) \to (11,-11)$
• $(-16,-16) \to (16,-16)$
• $(-6,-16) \to (6,-16)$

Step7: Step28 (rotate 180° clockwise)

For a point $(x,y)$, rotate 180° clockwise: $(-x,-y)$

• $(11,-11) \to (-11,11)$
• $(16,-16) \to (-16,16)$
• $(6,-16) \to (-6,16)$

Answer:

1. $(-11,11)$, $(-16,16)$, $(-16,6)$
2. $(11,11)$, $(16,16)$, $(6,16)$
3. $(-11,-11)$, $(-16,-16)$, $(-6,-16)$
4. $(11,-11)$, $(16,-16)$, $(6,-16)$
5. $(-11,11)$, $(-16,16)$, $(-6,16)$