This worksheet helps students practice translating shapes like trapezoids and parallelograms on a coordinate grid by following specific directional rules.

To solve these translation problems, we need to move each point of the shape according to the instructions.

Rule for Translations:
* Left/Right (x-axis): Move left means subtract from the x-coordinate. Move right means add to the x-coordinate.
* Up/Down (y-axis): Move up means add to the y-coordinate. Move down means subtract from the y-coordinate.

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

1. Trapezoid ABCD

Instruction: Translate 2 units left and 9 units up.
* Rule: $(x - 2, y + 9)$

Let's find the new coordinates for each vertex:
* Point A $(0, -2)$:
* $x: 0 - 2 = -2$
* $y: -2 + 9 = 7$
* New Point $A' = (-2, 7)$
* Point B $(2, -5)$:
* $x: 2 - 2 = 0$
* $y: -5 + 9 = 4$
* New Point $B' = (0, 4)$
* Point C $(-4, -5)$:
* $x: -4 - 2 = -6$
* $y: -5 + 9 = 4$
* New Point $C' = (-6, 4)$
* Point D $(-2, -2)$:
* $x: -2 - 2 = -4$
* $y: -2 + 9 = 7$
* New Point $D' = (-4, 7)$

Graphing: Plot points $(-2, 7), (0, 4), (-6, 4),$ and $(-4, 7)$ and connect them to form the new trapezoid.

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2. Trapezoid WXYZ

Instruction: Translate 7 units right and 1 unit down.
* Rule: $(x + 7, y - 1)$

Let's find the new coordinates:
* Point W $(3, 1)$:
* $x: 3 + 7 = 10$
* $y: 1 - 1 = 0$
* New Point $W' = (10, 0)$
* Point X $(2, 6)$:
* $x: 2 + 7 = 9$
* $y: 6 - 1 = 5$
* New Point $X' = (9, 5)$
* Point Y $(-1, 5)$:
* $x: -1 + 7 = 6$
* $y: 5 - 1 = 4$
* New Point $Y' = (6, 4)$
* Point Z $(-1, 1)$:
* $x: -1 + 7 = 6$
* $y: 1 - 1 = 0$
* New Point $Z' = (6, 0)$

Graphing: Plot points $(10, 0), (9, 5), (6, 4),$ and $(6, 0)$ and connect them.

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3. Parallelogram JKLM

Instruction: Translate 8 units right and 5 units up.
* Rule: $(x + 8, y + 5)$

Let's find the new coordinates:
* Point J $(-1, 1)$:
* $x: -1 + 8 = 7$
* $y: 1 + 5 = 6$
* New Point $J' = (7, 6)$
* Point K $(-4, -2)$:
* $x: -4 + 8 = 4$
* $y: -2 + 5 = 3$
* New Point $K' = (4, 3)$
* Point L $(-7, -2)$:
* $x: -7 + 8 = 1$
* $y: -2 + 5 = 3$
* New Point $L' = (1, 3)$
* Point M $(-4, 1)$:
* $x: -4 + 8 = 4$
* $y: 1 + 5 = 6$
* New Point $M' = (4, 6)$

Graphing: Plot points $(7, 6), (4, 3), (1, 3),$ and $(4, 6)$ and connect them.

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4. Parallelogram PQRS

Instruction: Translate 3 units left and 6 units down.
* Rule: $(x - 3, y - 6)$

Let's find the new coordinates:
* Point P $(0, -4)$:
* $x: 0 - 3 = -3$
* $y: -4 - 6 = -10$
* New Point $P' = (-3, -10)$
* Point Q $(-2, 3)$:
* $x: -2 - 3 = -5$
* $y: 3 - 6 = -3$
* New Point $Q' = (-5, -3)$
* Point R $(2, 3)$:
* $x: 2 - 3 = -1$
* $y: 3 - 6 = -3$
* New Point $R' = (-1, -3)$
* Point S $(4, -4)$:
* $x: 4 - 3 = 1$
* $y: -4 - 6 = -10$
* New Point $S' = (1, -10)$

Graphing: Plot points $(-3, -10), (-5, -3), (-1, -3),$ and $(1, -10)$ and connect them.

Final Answer:
The new coordinates for the translated figures are:
1. Trapezoid A'B'C'D': $A'(-2, 7), B'(0, 4), C'(-6, 4), D'(-4, 7)$
2. Trapezoid W'X'Y'Z': $W'(10, 0), X'(9, 5), Y'(6, 4), Z'(6, 0)$
3. Parallelogram J'K'L'M': $J'(7, 6), K'(4, 3), L'(1, 3), M'(4, 6)$
4. Parallelogram P'Q'R'S': $P'(-3, -10), Q'(-5, -3), R'(-1, -3), S'(1, -10)$