Geometry Worksheets | Transformations Worksheets - Free Printable

To solve these translation problems, we need to move each point of the green shape according to the instructions. A translation means sliding the shape without turning or flipping it.

Here is the step-by-step solution for each problem:

1) Translation: 3 right
* Original Points: The triangle has vertices at $(-2, -1)$, $(-2, -5)$, and $(0, -5)$.
* Rule: Add 3 to the x-coordinate ($x + 3$). Keep y the same.
* New Points:
* $(-2 + 3, -1) \rightarrow (1, -1)$
* $(-2 + 3, -5) \rightarrow (1, -5)$
* $(0 + 3, -5) \rightarrow (3, -5)$
* Result: Draw a triangle connecting $(1, -1)$, $(1, -5)$, and $(3, -5)$.

2) Translation: 2 right and 3 down
* Original Points: The quadrilateral has vertices at $(-4, 4)$, $(-1, 4)$, $(-1, 2)$, and $(-3, 2)$.
* Rule: Add 2 to x ($x + 2$) and subtract 3 from y ($y - 3$).
* New Points:
* $(-4 + 2, 4 - 3) \rightarrow (-2, 1)$
* $(-1 + 2, 4 - 3) \rightarrow (1, 1)$
* $(-1 + 2, 2 - 3) \rightarrow (1, -1)$
* $(-3 + 2, 2 - 3) \rightarrow (-1, -1)$
* Result: Draw the shape connecting $(-2, 1)$, $(1, 1)$, $(1, -1)$, and $(-1, -1)$.

3) Translation: 5 left
* Original Points: The triangle has vertices at $(1, -2)$, $(4, -3)$, and $(4, -5)$.
* Rule: Subtract 5 from the x-coordinate ($x - 5$). Keep y the same.
* New Points:
* $(1 - 5, -2) \rightarrow (-4, -2)$
* $(4 - 5, -3) \rightarrow (-1, -3)$
* $(4 - 5, -5) \rightarrow (-1, -5)$
* Result: Draw a triangle connecting $(-4, -2)$, $(-1, -3)$, and $(-1, -5)$.

4) Translation: 4 left and 3 down
* Original Points: The L-shape has outer vertices at $(2, 4)$, $(4, 4)$, $(4, 1)$, $(3, 1)$, $(3, 2)$, and $(2, 2)$.
* Rule: Subtract 4 from x ($x - 4$) and subtract 3 from y ($y - 3$).
* New Points:
* $(2 - 4, 4 - 3) \rightarrow (-2, 1)$
* $(4 - 4, 4 - 3) \rightarrow (0, 1)$
* $(4 - 4, 1 - 3) \rightarrow (0, -2)$
* $(3 - 4, 1 - 3) \rightarrow (-1, -2)$
* $(3 - 4, 2 - 3) \rightarrow (-1, -1)$
* $(2 - 4, 2 - 3) \rightarrow (-2, -1)$
* Result: Draw the L-shape using these new coordinates.

5) Translation: 4 left and 5 down
* Original Points: The quadrilateral has vertices at $(1, 3)$, $(3, 3)$, $(4, 1)$, and $(1, 1)$.
* Rule: Subtract 4 from x ($x - 4$) and subtract 5 from y ($y - 5$).
* New Points:
* $(1 - 4, 3 - 5) \rightarrow (-3, -2)$
* $(3 - 4, 3 - 5) \rightarrow (-1, -2)$
* $(4 - 4, 1 - 5) \rightarrow (0, -4)$
* $(1 - 4, 1 - 5) \rightarrow (-3, -4)$
* Result: Draw the shape connecting $(-3, -2)$, $(-1, -2)$, $(0, -4)$, and $(-3, -4)$.

6) Translation: 3 right and 4 up
* Original Points: The triangle has vertices at $(-2, -1)$, $(-1, -3)$, and $(1, -2)$.
* Rule: Add 3 to x ($x + 3$) and add 4 to y ($y + 4$).
* New Points:
* $(-2 + 3, -1 + 4) \rightarrow (1, 3)$
* $(-1 + 3, -3 + 4) \rightarrow (2, 1)$
* $(1 + 3, -2 + 4) \rightarrow (4, 2)$
* Result: Draw a triangle connecting $(1, 3)$, $(2, 1)$, and $(4, 2)$.

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