Translations worksheet (transformation of shapes) - Free Printable

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

Key Rules for Translation:
* Right: Add to the x-coordinate (move right).
* Left: Subtract from the x-coordinate (move left).
* Up: Add to the y-coordinate (move up).
* Down: Subtract from the y-coordinate (move down).

Let's break down each problem step-by-step by picking key points (vertices) on the original shape and moving them.

1) 5 units down and 4 units right

* Original Shape: A "U" shape or bracket in the top-left quadrant. Let's pick the bottom-left corner at $(-3, 2)$.
* Move Right 4: $-3 + 4 = 1$. The new x is $1$.
* Move Down 5: $2 - 5 = -3$. The new y is $-3$.
* New Point: $(1, -3)$.
* Check another point: Top-left corner at $(-3, 4)$.
* Right 4: $-3 + 4 = 1$.
* Down 5: $4 - 5 = -1$.
* New Point: $(1, -1)$.
* Result: The shape moves into the fourth quadrant (bottom-right area relative to origin, but specifically crossing axes). The bottom edge will be at $y = -3$ and top edge at $y = -1$. The left side will be at $x = 1$ and right side at $x = 3$.

2) 2 units left and 6 units down

* Original Shape: An L-shape in the first quadrant. Let's pick the inner corner at $(2, 2)$.
* Move Left 2: $2 - 2 = 0$. The new x is $0$ (on the y-axis).
* Move Down 6: $2 - 6 = -4$. The new y is $-4$.
* New Point: $(0, -4)$.
* Check top-left corner: Original at $(1, 5)$.
* Left 2: $1 - 2 = -1$.
* Down 6: $5 - 6 = -1$.
* New Point: $(-1, -1)$.
* Result: The shape moves mostly into the third and fourth quadrants. The vertical part of the L will straddle the y-axis.

3) 7 units left

* Original Shape: A downward arrowhead in the fourth quadrant. Let's pick the tip at $(3, -3)$.
* Move Left 7: $3 - 7 = -4$. The new x is $-4$.
* Vertical Move: None. Y stays $-3$.
* New Point: $(-4, -3)$.
* Check top-right corner: Original at $(4, -1)$.
* Left 7: $4 - 7 = -3$.
* New Point: $(-3, -1)$.
* Result: The entire shape shifts horizontally to the left, ending up in the third quadrant.

4) 2 units left and 3 units up

* Original Shape: A triangle/trapezoid combo in the fourth quadrant. Let's pick the bottom-right corner at $(3, -3)$.
* Move Left 2: $3 - 2 = 1$. New x is $1$.
* Move Up 3: $-3 + 3 = 0$. New y is $0$ (on the x-axis).
* New Point: $(1, 0)$.
* Check top vertex: Original at $(2, -1)$.
* Left 2: $2 - 2 = 0$.
* Up 3: $-1 + 3 = 2$.
* New Point: $(0, 2)$.
* Result: The shape moves up and slightly left, sitting mostly in the first quadrant with one point on the y-axis and one on the x-axis.

5) 6 units up and 8 units right

* Original Shape: A rectangle in the third quadrant. Bottom-left corner at $(-5, -3)$.
* Move Right 8: $-5 + 8 = 3$. New x is $3$.
* Move Up 6: $-3 + 6 = 3$. New y is $3$.
* New Point: $(3, 3)$.
* Check top-right corner: Original at $(-2, -1)$.
* Right 8: $-2 + 8 = 6$.
* Up 6: $-1 + 6 = 5$.
* New Point: $(6, 5)$.
* Result: The rectangle moves far into the first quadrant.

6) 1 unit right and 5 units up

* Original Shape: A house/pentagon in the third/fourth quadrant area. Let's pick the bottom-left corner at $(-2, -4)$.
* Move Right 1: $-2 + 1 = -1$. New x is $-1$.
* Move Up 5: $-4 + 5 = 1$. New y is $1$.
* New Point: $(-1, 1)$.
* Check peak: Original at $(-1, -1)$.
* Right 1: $-1 + 1 = 0$.
* Up 5: $-1 + 5 = 4$.
* New Point: $(0, 4)$.
* Result: The shape moves up into the second and first quadrants. The peak touches the y-axis.

7) 3 units up and 1 unit left

* Original Shape: A pentagon pointing left in the third quadrant. Let's pick the leftmost tip at $(-4, -2)$.
* Move Left 1: $-4 - 1 = -5$. New x is $-5$.
* Move Up 3: $-2 + 3 = 1$. New y is $1$.
* New Point: $(-5, 1)$.
* Check bottom-right corner: Original at $(-1, -3)$.
* Left 1: $-1 - 1 = -2$.
* Up 3: $-3 + 3 = 0$.
* New Point: $(-2, 0)$.
* Result: The shape moves up and slightly left, staying in the second and third quadrants.

8) 5 units down

* Original Shape: A stepped square in the second quadrant. Let's pick the top-left corner at $(-3, 4)$.
* Move Down 5: $4 - 5 = -1$. New y is $-1$.
* Horizontal Move: None. X stays $-3$.
* New Point: $(-3, -1)$.
* Check bottom-right corner: Original at $(-1, 1)$.
* Down 5: $1 - 5 = -4$.
* New Point: $(-1, -4)$.
* Result: The shape shifts straight down, crossing the x-axis into the third and fourth quadrants.

9) 2 units down and 4 units left

* Original Shape: A diamond with an X inside in the first quadrant. Center/intersection at $(2, 2)$.
* Move Left 4: $2 - 4 = -2$. New x is $-2$.
* Move Down 2: $2 - 2 = 0$. New y is $0$.
* New Point: $(-2, 0)$.
* Check top vertex: Original at $(2, 4)$.
* Left 4: $2 - 4 = -2$.
* Down 2: $4 - 2 = 2$.
* New Point: $(-2, 2)$.
* Check bottom vertex: Original at $(2, 0)$.
* Left 4: $2 - 4 = -2$.
* Down 2: $0 - 2 = -2$.
* New Point: $(-2, -2)$.
* Result: The shape moves to the left, centered on the line $x = -2$, spanning from $y = 2$ to $y = -2$.

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Final Answer:
Here are the coordinates for the key vertices of the translated shapes to help you graph them accurately:

1) 5 units down, 4 units right
* Bottom-Left Corner: $(1, -3)$
* Top-Left Corner: $(1, -1)$
* Top-Right Corner: $(3, -1)$
* Bottom-Right Corner: $(3, -3)$
*(The shape is now a U-shape opening upwards, located between x=1 to 3 and y=-3 to -1)*

2) 2 units left, 6 units down
* Inner Corner: $(0, -4)$
* Top-Left Corner: $(-1, -1)$
* Bottom-Left Corner: $(-1, -4)$
* Bottom-Right Corner: $(2, -4)$
*(The vertical bar is on the y-axis and to its left; the horizontal bar extends to the right)*

3) 7 units left
* Tip of Arrow: $(-4, -3)$
* Top-Right Corner: $(-3, -1)$
* Top-Left Corner: $(-5, -1)$
*(The arrow points down, shifted entirely into the third quadrant)*

4) 2 units left, 3 units up
* Bottom-Right Corner: $(1, 0)$
* Top Vertex: $(0, 2)$
* Bottom-Left Corner: $(-1, 0)$ -- *Wait, original bottom left was (1,-3)? No, looking at grid: Original shape has vertices approx (1,-3), (3,-3), (3,-1), (2,-1), (1,-2)? Let's re-read grid 4 carefully.*
*Correction for #4 based on visual grid:*
Original Vertices appear to be: $(1, -3), (3, -3), (3, -1), (1, -1)$ is a rectangle? No, it's a triangle on top of a square?
Let's look at Grid 4 again. It looks like a triangle with vertices $(1, -1), (3, -1), (3, -3)$? No, there is a diagonal.
Vertices: $(1, -3), (3, -3), (3, -1), (1, -1)$ is not right.
It looks like a right triangle with vertices $(1, -3), (3, -3), (3, -1)$? And a square below?
Actually, let's just use the translation vector on visible points.
Point A (bottom right): $(3, -3) \rightarrow (3-2, -3+3) = (1, 0)$.
Point B (top right): $(3, -1) \rightarrow (3-2, -1+3) = (1, 2)$.
Point C (bottom left of triangle part): $(1, -1) \rightarrow (1-2, -1+3) = (-1, 2)$.
Point D (bottom left of square part): $(1, -3) \rightarrow (1-2, -3+3) = (-1, 0)$.
So the new shape has corners at $(1,0), (1,2), (-1,2), (-1,0)$. It is a square/rectangle block now?
Looking closely at image 4: It is a square from $(1,-3)$ to $(2,-2)$? No.
It is a shape composed of a square $(1,-3)$ to $(2,-2)$ and a triangle?
Let's assume standard grid lines.
Shape 4 Vertices: $(1, -3), (2, -3), (2, -2), (3, -1), (1, -1)$. This forms a polygon.
Translation: $x-2, y+3$.
$(1, -3) \rightarrow (-1, 0)$
$(2, -3) \rightarrow (0, 0)$
$(2, -2) \rightarrow (0, 1)$
$(3, -1) \rightarrow (1, 2)$
$(1, -1) \rightarrow (-1, 2)$
Graph these points: $(-1,0), (0,0), (0,1), (1,2), (-1,2)$. Connect them in order.

5) 6 units up, 8 units right
* Bottom-Left: $(-5, -3) \rightarrow (3, 3)$
* Bottom-Right: $(-2, -3) \rightarrow (6, 3)$
* Top-Right: $(-2, -1) \rightarrow (6, 5)$
* Top-Left: $(-5, -1) \rightarrow (3, 5)$
*(Draw a rectangle with these corners)*

6) 1 unit right, 5 units up
* Bottom-Left: $(-2, -4) \rightarrow (-1, 1)$
* Bottom-Right: $(0, -4) \rightarrow (1, 1)$
* Top-Right (shoulder): $(0, -2) \rightarrow (1, 3)$
* Peak: $(-1, -1) \rightarrow (0, 4)$
* Top-Left (shoulder): $(-2, -2) \rightarrow (-1, 3)$
*(Draw this "house" shape using these new coordinates)*

7) 3 units up, 1 unit left
* Left Tip: $(-4, -2) \rightarrow (-5, 1)$
* Top-Left: $(-2, -1) \rightarrow (-3, 2)$
* Top-Right: $(-1, -1) \rightarrow (-2, 2)$
* Bottom-Right: $(-1, -3) \rightarrow (-2, 0)$
* Bottom-Left: $(-2, -3) \rightarrow (-3, 0)$
*(Draw this pentagon using these new coordinates)*

8) 5 units down
* Top-Left: $(-3, 4) \rightarrow (-3, -1)$
* Top-Right (inner): $(-2, 4) \rightarrow (-2, -1)$ ... wait, shape is stepped.
Let's trace perimeter:
$(-3, 4) \rightarrow (-3, -1)$
$(-1, 4) \rightarrow (-1, -1)$ -- Top right corner of top block? No, shape is:
Block 1: $x[-3,-1], y[2,4]$. Block 2: $x[-3,-2], y[1,2]$?
Let's just shift every visible vertex down by 5.
Top Edge $y=4 \rightarrow y=-1$.
Middle Step $y=2 \rightarrow y=-3$.
Bottom Edge $y=1 \rightarrow y=-4$.
Left Edge $x=-3$. Right Edges $x=-1$ and $x=-2$.
*(Draw the stepped shape shifted down so the top is at y=-1 and bottom is at y=-4)*

9) 2 units down, 4 units left
* Center: $(2, 2) \rightarrow (-2, 0)$
* Top: $(2, 4) \rightarrow (-2, 2)$
* Bottom: $(2, 0) \rightarrow (-2, -2)$
* Left: $(0, 2) \rightarrow (-4, 0)$
* Right: $(4, 2) \rightarrow (0, 0)$
*(Draw a diamond centered at $(-2,0)$ with vertices at $(-2,2), (-2,-2), (-4,0), (0,0)$. Draw an X connecting opposite vertices)*