To solve this problem, we need to find the coordinates of each space object on the grid and then apply the translation rules given in the table on the right side of the image.
Step 1: Understand how to read coordinates
Coordinates are written as $(x, y)$.
- The first number ($x$) tells you how far to go across from the left (horizontal axis).
- The second number ($y$) tells you how far to go up from the bottom (vertical axis).
Step 2: Identify the Original Coordinates
Let's look at each object on the main grid and find its starting position $(x, y)$:
1.
Earth (Blue/Green Planet):
- Go across to $6$, go up to $9$.
- Coordinate: $(6, 9)$
2.
Gray Planet (Top Right):
- Go across to $10$, go up to $8$.
- Coordinate: $(10, 8)$
3.
Satellite (Bottom Right):
- Go across to $9$, go up to $1$.
- Coordinate: $(9, 1)$
4.
Astronaut:
- Go across to $8$, go up to $5$.
- Coordinate: $(8, 5)$
5.
UFO (Flying Saucer):
- Go across to $5$, go up to $6$.
- Coordinate: $(5, 6)$
6.
Small Gray Asteroid/Planet (Bottom Left):
- Go across to $4$, go up to $2$.
- Coordinate: $(4, 2)$
7.
Space Shuttle (Left):
- Go across to $1$, go up to $3$.
- Coordinate: $(1, 3)$
8.
Rocket Ship (Top Left):
- Go across to $2$, go up to $9$.
- Coordinate: $(2, 9)$
Step 3: Apply the Translations
Now we use the rules from the "Translation" column in the table to find the new coordinates.
-
"Left" means subtract from the x-coordinate.
-
"Right" means add to the x-coordinate.
-
"Up" means add to the y-coordinate.
-
"Down" means subtract from the y-coordinate.
Let's calculate the new position for each object based on the rows in the table:
1.
Earth: Rule is `Left 3, Down 7`
- New $x = 6 - 3 = 3$
- New $y = 9 - 7 = 2$
- Final Coordinate:
$(3, 2)$
2.
Gray Planet: Rule is `Right 2, Down 4`
- New $x = 10 + 2 = 12$
- New $y = 8 - 4 = 4$
- Final Coordinate:
$(12, 4)$
3.
Satellite: Rule is `Left 4, Up 3`
- New $x = 9 - 4 = 5$
- New $y = 1 + 3 = 4$
- Final Coordinate:
$(5, 4)$
4.
Astronaut: Rule is `Right 1, Up 1`
- New $x = 8 + 1 = 9$
- New $y = 5 + 1 = 6$
- Final Coordinate:
$(9, 6)$
5.
UFO: Rule is `Left 5, Down 3`
- New $x = 5 - 5 = 0$
- New $y = 6 - 3 = 3$
- Final Coordinate:
$(0, 3)$
6.
Small Gray Asteroid: Rule is `Left 2, Down 2`
- New $x = 4 - 2 = 2$
- New $y = 2 - 2 = 0$
- Final Coordinate:
$(2, 0)$
7.
Space Shuttle: Rule is `Right 4, Up 4`
- New $x = 1 + 4 = 5$
- New $y = 3 + 4 = 7$
- Final Coordinate:
$(5, 7)$
8.
Rocket Ship: Rule is `Right 1, Up 1`
- New $x = 2 + 1 = 3$
- New $y = 9 + 1 = 10$
- Final Coordinate:
$(3, 10)$
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Final Answer:
Here are the completed coordinates for the table:
| Object | Original Coordinate | Translation | Ending Coordinate |
| :--- | :---: | :--- | :---: |
| Earth | $(6, 9)$ | Left 3, Down 7 |
$(3, 2)$ |
| Gray Planet | $(10, 8)$ | Right 2, Down 4 |
$(12, 4)$ |
| Satellite | $(9, 1)$ | Left 4, Up 3 |
$(5, 4)$ |
| Astronaut | $(8, 5)$ | Right 1, Up 1 |
$(9, 6)$ |
| UFO | $(5, 6)$ | Left 5, Down 3 |
$(0, 3)$ |
| Small Asteroid | $(4, 2)$ | Left 2, Down 2 |
$(2, 0)$ |
| Space Shuttle | $(1, 3)$ | Right 4, Up 4 |
$(5, 7)$ |
| Rocket Ship | $(2, 9)$ | Right 1, Up 1 |
$(3, 10)$ |
Parent Tip: Review the logic above to help your child master the concept of translations on a coordinate plane worksheet.
