Geometry Worksheets | Transformations Worksheets - Free Printable

To solve these translation problems, we need to move each shape on the grid according to the instructions given. A translation means sliding the shape without turning or flipping it. We will move every corner (vertex) of the shape by the same amount and direction.

Let's go through each problem one by one:

Problem 1: Translation 3 right
* Original Shape: A triangle in the third quadrant.
* Top vertex: (-4, 0)
* Bottom-left vertex: (-4, -4)
* Bottom-right vertex: (-2, -4)
* Instruction: Move 3 units to the right. This means we add 3 to the x-coordinate of each point.
* New Coordinates:
* Top vertex: (-4 + 3, 0) = (-1, 0)
* Bottom-left vertex: (-4 + 3, -4) = (-1, -4)
* Bottom-right vertex: (-2 + 3, -4) = (1, -4)
* Result: The new triangle has vertices at (-1, 0), (-1, -4), and (1, -4).

Problem 2: Translation 2 right and 3 down
* Original Shape: A quadrilateral in the second quadrant.
* Top-left vertex: (-5, 4)
* Top-right vertex: (-2, 4)
* Bottom-right vertex: (-2, 2)
* Bottom-left vertex: (-3, 2)
* Instruction: Move 2 units right (add 2 to x) and 3 units down (subtract 3 from y).
* New Coordinates:
* Top-left: (-5 + 2, 4 - 3) = (-3, 1)
* Top-right: (-2 + 2, 4 - 3) = (0, 1)
* Bottom-right: (-2 + 2, 2 - 3) = (0, -1)
* Bottom-left: (-3 + 2, 2 - 3) = (-1, -1)
* Result: The new shape has vertices at (-3, 1), (0, 1), (0, -1), and (-1, -1).

Problem 3: Translation 5 left
* Original Shape: A triangle in the fourth quadrant.
* Top vertex: (4, -2)
* Left vertex: (2, -3)
* Bottom vertex: (4, -4)
* Instruction: Move 5 units left. This means we subtract 5 from the x-coordinate of each point.
* New Coordinates:
* Top vertex: (4 - 5, -2) = (-1, -2)
* Left vertex: (2 - 5, -3) = (-3, -3)
* Bottom vertex: (4 - 5, -4) = (-1, -4)
* Result: The new triangle has vertices at (-1, -2), (-3, -3), and (-1, -4).

Problem 4: Translation 4 left and 3 down
* Original Shape: An L-shaped polygon in the first quadrant.
* Top-left: (2, 5)
* Top-right: (4, 5)
* Inner corner 1: (4, 3)
* Inner corner 2: (3, 3)
* Bottom-right: (3, 1)
* Bottom-left: (2, 1)
* Instruction: Move 4 units left (subtract 4 from x) and 3 units down (subtract 3 from y).
* New Coordinates:
* Top-left: (2 - 4, 5 - 3) = (-2, 2)
* Top-right: (4 - 4, 5 - 3) = (0, 2)
* Inner corner 1: (4 - 4, 3 - 3) = (0, 0)
* Inner corner 2: (3 - 4, 3 - 3) = (-1, 0)
* Bottom-right: (3 - 4, 1 - 3) = (-1, -2)
* Bottom-left: (2 - 4, 1 - 3) = (-2, -2)
* Result: The new shape has vertices at (-2, 2), (0, 2), (0, 0), (-1, 0), (-1, -2), and (-2, -2).

Problem 5: Translation 4 left and 5 down
* Original Shape: A trapezoid in the first quadrant.
* Top-left: (2, 4)
* Top-right: (4, 4)
* Bottom-right: (3, 2)
* Bottom-left: (2, 1)
* Instruction: Move 4 units left (subtract 4 from x) and 5 units down (subtract 5 from y).
* New Coordinates:
* Top-left: (2 - 4, 4 - 5) = (-2, -1)
* Top-right: (4 - 4, 4 - 5) = (0, -1)
* Bottom-right: (3 - 4, 2 - 5) = (-1, -3)
* Bottom-left: (2 - 4, 1 - 5) = (-2, -4)
* Result: The new shape has vertices at (-2, -1), (0, -1), (-1, -3), and (-2, -4).

Problem 6: Translation 3 right and 4 up
* Original Shape: A triangle in the third quadrant.
* Top vertex: (-1, 0)
* Left vertex: (-4, -3)
* Bottom vertex: (-2, -4)
* Instruction: Move 3 units right (add 3 to x) and 4 units up (add 4 to y).
* New Coordinates:
* Top vertex: (-1 + 3, 0 + 4) = (2, 4)
* Left vertex: (-4 + 3, -3 + 4) = (-1, 1)
* Bottom vertex: (-2 + 3, -4 + 4) = (1, 0)
* Result: The new triangle has vertices at (2, 4), (-1, 1), and (1, 0).

Final Answer:
1) Triangle vertices: (-1, 0), (-1, -4), (1, -4)
2) Quadrilateral vertices: (-3, 1), (0, 1), (0, -1), (-1, -1)
3) Triangle vertices: (-1, -2), (-3, -3), (-1, -4)
4) Polygon vertices: (-2, 2), (0, 2), (0, 0), (-1, 0), (-1, -2), (-2, -2)
5) Trapezoid vertices: (-2, -1), (0, -1), (-1, -3), (-2, -4)
6) Triangle vertices: (2, 4), (-1, 1), (1, 0)