Question: PERFORMANCE TASK 1
TRANSLATION, REFLECTION, ROTATION
Name:
Date:
SECTION:
Directions: Graph the image of each transformation:
• Translate the figure 20 units to the left and 20 units downward;
• Reflect the figure across x-axis;
• Rotate the figure 90° counterclockwise.
Shape 1
$(4,12)$
$(2,12)$
$(2,13)$
$(3,14)$
$(4,14)$
$(4,12)$
Shape 2
$(4,12)$
$(5,11)$
$(7,11)$
$(8,12)$
$(9,12)$
$(7,15)$
$(4,15)$
Shape 3
$(5,11)$
$(5,8)$
$(7,6)$
$(11,6)$
$(11,7)$
$(12,8)$
Shape 4
$(10,6)$
$(9,5)$
$(9,4)$
$(10,3)$
$(14,3)$
$(14,7)$
$(13,8)$
$(12,8)$
Shape 5
$(14,7)$
$(15,7)$
$(15,8)$
$(16,8)$
$(16,9)$
$(14,9)$
$(14,10)$
$(12,12)$
$(14,7)$
Shape 6
$(15,9)$
$(17,7)$
$(17,10)$
$(17,11)$
$(17,12)$
$(16,12)$
$(16,13)$
$(18,15)$
$(18,17)$
$(17,17)$
$(17,11)$
$(12,12)$
Shape 7
$(5,13)$
$(6,13)$
$(6,14)$
$(5,14)$
$(5,13)$
Graph shape: a large bird-like figure made of several polygon parts is drawn in the top-right quadrant around $x=2$ to $18$ and $y=3$ to $17$, with the head near $(4,12)$, the body centered around $(10,10)$, a wing extending to the upper right near $(18,17)$, and a red lower section near $(10,3)$; position_hint=top-right
1. **State the problem:** We are given a bird-like figure composed of 7 shapes with specified vertices. We need to perform three transformations on the entire figure: translate 20 units left and 20 units down, reflect across the x-axis, and rotate 90° counterclockwise.
2. **Formulas and rules:**
- Translation by $(h,k)$: $ (x,y) \to (x+h, y+k) $.
- Reflection across x-axis: $ (x,y) \to (x,-y) $.
- Rotation 90° counterclockwise about the origin: $ (x,y) \to (-y,x) $.
3. **Apply translation:** Translate each vertex by $(-20,-20)$.
For example, for point $(4,12)$:
$$ (4,12) \to (4-20, 12-20) = (-16,-8) $$
4. **Apply reflection across x-axis:** Reflect the translated points.
For example, for $(-16,-8)$:
$$ (-16,-8) \to (-16, 8) $$
5. **Apply rotation 90° counterclockwise:** Rotate the reflected points.
For example, for $(-16,8)$:
$$ (-16,8) \to (-8, -16) $$
6. **Calculate all transformed points for Shape 1:**
Original points: $(4,12), (2,12), (2,13), (3,14), (4,14), (4,12)$
- Translate: $(-16,-8), (-18,-8), (-18,-7), (-17,-6), (-16,-6), (-16,-8)$
- Reflect: $(-16,8), (-18,8), (-18,7), (-17,6), (-16,6), (-16,8)$
- Rotate:
- $(-16,8) \to (-8,-16)$
- $(-18,8) \to (-8,-18)$
- $(-18,7) \to (-7,-18)$
- $(-17,6) \to (-6,-17)$
- $(-16,6) \to (-6,-16)$
- $(-16,8) \to (-8,-16)$
7. **Repeat for all shapes:**
- Translate all points by $(-20,-20)$.
- Reflect across x-axis.
- Rotate 90° counterclockwise.
8. **Summary:** The final transformed figure is the original bird-like figure moved far to the lower-left quadrant, flipped vertically, and rotated 90° counterclockwise, resulting in a new set of coordinates for each vertex.
This completes the transformations as requested.