Translations worksheet with six problems illustrating how shapes move on a coordinate grid.

Since the user has set all options (ExplainAnswer, TeachTopic, GeneratePractice) to false, I will proceed directly to providing the final answer based on the task shown in the image.

The task is to perform translations on geometric shapes plotted on a coordinate grid. A translation moves every point of a shape by the same distance in the same direction.

Let's solve each problem step by step:

Problem 1: Translation: 3 right
- Original shape vertices: (-4, -2), (-4, -5), (-2, -5), (-2, -3)
- Move each point 3 units to the right (add 3 to x-coordinate):
- (-4+3, -2) = (-1, -2)
- (-4+3, -5) = (-1, -5)
- (-2+3, -5) = (1, -5)
- (-2+3, -3) = (1, -3)
- New vertices: (-1, -2), (-1, -5), (1, -5), (1, -3)

Problem 2: Translation: 2 right and 3 down
- Original shape vertices: (-5, 5), (-5, 3), (-3, 3), (-3, 5)
- Move each point 2 right (add 2 to x) and 3 down (subtract 3 from y):
- (-5+2, 5-3) = (-3, 2)
- (-5+2, 3-3) = (-3, 0)
- (-3+2, 3-3) = (-1, 0)
- (-3+2, 5-3) = (-1, 2)
- New vertices: (-3, 2), (-3, 0), (-1, 0), (-1, 2)

Problem 3: Translation: 5 left
- Original shape vertices: (2, -2), (2, -4), (4, -3)
- Move each point 5 left (subtract 5 from x-coordinate):
- (2-5, -2) = (-3, -2)
- (2-5, -4) = (-3, -4)
- (4-5, -3) = (-1, -3)
- New vertices: (-3, -2), (-3, -4), (-1, -3)

Problem 4: Translation: 4 left and 3 down
- Original shape vertices: (2, 4), (4, 4), (4, 2), (3, 2), (3, 3), (2, 3)
- Move each point 4 left (subtract 4 from x) and 3 down (subtract 3 from y):
- (2-4, 4-3) = (-2, 1)
- (4-4, 4-3) = (0, 1)
- (4-4, 2-3) = (0, -1)
- (3-4, 2-3) = (-1, -1)
- (3-4, 3-3) = (-1, 0)
- (2-4, 3-3) = (-2, 0)
- New vertices: (-2, 1), (0, 1), (0, -1), (-1, -1), (-1, 0), (-2, 0)

Problem 5: Translation: 4 left and 5 down
- Original shape vertices: (2, 2), (2, 4), (4, 4), (4, 2)
- Move each point 4 left (subtract 4 from x) and 5 down (subtract 5 from y):
- (2-4, 2-5) = (-2, -3)
- (2-4, 4-5) = (-2, -1)
- (4-4, 4-5) = (0, -1)
- (4-4, 2-5) = (0, -3)
- New vertices: (-2, -3), (-2, -1), (0, -1), (0, -3)

Problem 6: Translation: 3 right and 4 up
- Original shape vertices: (-3, -3), (-1, -3), (-1, -1), (-3, -1)
- Move each point 3 right (add 3 to x) and 4 up (add 4 to y):
- (-3+3, -3+4) = (0, 1)
- (-1+3, -3+4) = (2, 1)
- (-1+3, -1+4) = (2, 3)
- (-3+3, -1+4) = (0, 3)
- New vertices: (0, 1), (2, 1), (2, 3), (0, 3)

Final Answer:
1) New vertices: (-1, -2), (-1, -5), (1, -5), (1, -3)
2) New vertices: (-3, 2), (-3, 0), (-1, 0), (-1, 2)
3) New vertices: (-3, -2), (-3, -4), (-1, -3)
4) New vertices: (-2, 1), (0, 1), (0, -1), (-1, -1), (-1, 0), (-2, 0)
5) New vertices: (-2, -3), (-2, -1), (0, -1), (0, -3)
6) New vertices: (0, 1), (2, 1), (2, 3), (0, 3)