Question

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

Explanation:

First, we correct the errors in the prior steps and complete all transformations step-by-step:

Step 1: Correct #22 (Translate #21 down 22)

Subtract 22 from each y-coordinate.
Original points: $(11,11), (16,16), (16,6)$
New points:
$(11, 11-22)=(11,-11)$, $(16,16-22)=(16,-6)$, $(16,6-22)=(16,-16)$

Step 2: Correct #23 (Reflect #22 over y-axis)

Negate each x-coordinate.
Points from #22: $(11,-11), (16,-6), (16,-16)$
New points:
$(-11,-11)$, $(-16,-6)$, $(-16,-16)$

Step 3: Complete #24 (Translate #23 up 22)

Add 22 to each y-coordinate.
Points from #23: $(-11,-11), (-16,-6), (-16,-16)$
New points:
$(-11, -11+22)=(-11,11)$, $(-16, -6+22)=(-16,16)$, $(-16, -16+22)=(-16,6)$

Step 4: Complete #25 (Rotate #24 90° clockwise)

Use rotation rule: $(x,y) \to (y,-x)$
Points from #24: $(-11,11), (-16,16), (-16,6)$
New points:
$(11,11)$, $(16,16)$, $(6,16)$

Step 5: Complete #26 (Rotate #25 180° clockwise)

Use rotation rule: $(x,y) \to (-x,-y)$
Points from #25: $(11,11), (16,16), (6,16)$
New points:
$(-11,-11)$, $(-16,-16)$, $(-6,-16)$

Step 6: Complete #27 (Reflect #26 over y-axis)

Negate each x-coordinate.
Points from #26: $(-11,-11), (-16,-16), (-6,-16)$
New points:
$(11,-11)$, $(16,-16)$, $(6,-16)$

Step 7: Complete #28 (Rotate #27 180° clockwise)

Use rotation rule: $(x,y) \to (-x,-y)$
Points from #27: $(11,-11), (16,-16), (6,-16)$
New points:
$(-11,11)$, $(-16,16)$, $(-6,16)$

Answer:

1. $(11,-11)$ $(16,-6)$ $(16,-16)$
2. $(-11,-11)$ $(-16,-6)$ $(-16,-16)$
3. $(-11,11)$ $(-16,16)$ $(-16,6)$
4. $(11,11)$ $(16,16)$ $(6,16)$
5. $(-11,-11)$ $(-16,-16)$ $(-6,-16)$
6. $(11,-11)$ $(16,-16)$ $(6,-16)$
7. $(-11,11)$ $(-16,16)$ $(-6,16)$