Translation Worksheets | Grade1to6.com - Free Printable

Let’s solve each translation step by step.

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Top Left: Translations: 4 right.

We have a triangle with vertices at approximately:
- (-5, -4)
- (-3, -4)
- (-4, -3)

To translate 4 right, we add 4 to the x-coordinate of each point.

New points:
- (-5 + 4, -4) = (-1, -4)
- (-3 + 4, -4) = (1, -4)
- (-4 + 4, -3) = (0, -3)

So the new triangle will be drawn with those three points.

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Top Right: Translations: 3 right and 2 down.

We have a square with corners at:
- (-4, 4), (-3, 4), (-3, 3), (-4, 3)

Translate 3 right: add 3 to x
Translate 2 down: subtract 2 from y

New points:
- (-4+3, 4-2) = (-1, 2)
- (-3+3, 4-2) = (0, 2)
- (-3+3, 3-2) = (0, 1)
- (-4+3, 3-2) = (-1, 1)

Draw the square using these new coordinates.

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Bottom Left: Translations: 3 left.

We have a hexagon centered around x=4, y=2. Let’s pick key points — for example, its rightmost point is at (5, 2), leftmost at (3, 2), top at (4, 3), bottom at (4, 1).

Actually, looking closely, it's symmetric. Let’s take one vertex: say (5, 2). Translate 3 left → subtract 3 from x.

But better to use all visible vertices. From grid:

Approximate vertices of hexagon:
- (3, 2)
- (4, 3)
- (5, 2)
- (5, 1)
- (4, 0) ← wait, no — looking again, it goes from y=1 to y=3? Actually, let me check:

From image: Hexagon spans x=3 to x=5, y=1 to y=3? Wait — actually, center seems to be at (4,2), and it touches:

Left: (3,2)
Right: (5,2)
Top: (4,3)
Bottom: (4,1)
And diagonals? Actually, regular hexagon might have more points, but since it’s on grid, likely vertices are:

(3,2), (4,3), (5,2), (5,1), (4,0)? No — that doesn’t match. Looking again — in the image, the hexagon is drawn such that:

It has flat top and bottom? Or pointy?

Actually, from the drawing, it looks like a regular hexagon oriented with horizontal sides. So vertices:

Top-left: (3.5, 3) — but we need integer coords? Hmm.

Wait — perhaps easier: just move every point 3 units left.

Since the whole shape moves, we can take any reference point. For example, the center appears to be at (4,2). Move 3 left → (1,2). Then redraw the same shape centered there.

But to be precise, let’s list actual grid points touched.

Looking carefully: The hexagon covers:

- At y=3: x=4 only? No — actually, from image, at y=3, it spans x=3.5 to 4.5? But since it’s on grid lines, maybe vertices are at:

Actually, let’s assume the hexagon has vertices at:

(3,2), (4,3), (5,2), (5,1), (4,0), (3,1) — but that would go to y=0, which isn't shown. In the image, the hexagon is between y=1 and y=3.

Better approach: Since it’s a translation, we don’t need exact vertices — just shift the entire figure 3 units left.

Original position: mostly between x=3 and x=5. After moving 3 left: between x=0 and x=2.

Center was at x=4 → now at x=1.

So draw identical hexagon centered at (1,2).

Vertices would be:

(0,2), (1,3), (2,2), (2,1), (1,0)? Again, y=0 may be out.

Wait — in original, lowest y is 1? Let me re-express.

Actually, from the image, the hexagon sits with:

- Top side: from (3.5,3) to (4.5,3) — but since grid is integer, perhaps it's drawn with corners at half-integers? That complicates.

Alternative: Just count squares.

The hexagon is located so that its leftmost point is at x=3, rightmost at x=5, top at y=3, bottom at y=1.

After translating 3 left:

Leftmost: x=0, rightmost: x=2, top y=3, bottom y=1.

So draw same shape shifted left by 3.

For accuracy, if original had a corner at (3,2), new is (0,2); (4,3)→(1,3); (5,2)→(2,2); (5,1)→(2,1); (4,0) not present — actually, bottom is at y=1, so (4,1)→(1,1); and (3,1)→(0,1).

Yes — so vertices become:

(0,2), (1,3), (2,2), (2,1), (1,1), (0,1) — but that’s not symmetric.

I think I’m overcomplicating. For school level, they expect you to move the whole shape without changing size or orientation.

So: take the hexagon as drawn, and slide it 3 boxes to the left. Every point decreases x by 3.

Final position: same shape, now centered around x=1 instead of x=4.

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Bottom Right: Translations: 4 right and 3 down.

Shape is an L-tetromino or similar. Let’s find its coordinates.

From image: It occupies:

- From x=-5 to x=-2, y=2 to y=5? Let’s see:

Specifically:

Points included:

(-5,3), (-5,2), (-4,2), (-3,2), (-3,3), (-3,4), (-2,4), (-2,5)? Wait — let's trace:

Actually, looking:

At y=5: x=-3 and x=-2? No — at y=5, only x=-3? Let me describe:

The shape has:

- A vertical part: from y=2 to y=5 at x=-3? And horizontal parts.

Better: List all filled squares.

Assume each cell is identified by bottom-left corner or center? Usually in such grids, we consider the coordinate of the lower-left corner of each unit square.

But to simplify, let’s take the bounding box.

The shape spans:

x from -5 to -2 (width 4)

y from 2 to 5 (height 4)

Specific cells filled:

Row y=5: x=-3, x=-2? From image: at top, it has two blocks: at x=-3 and x=-2 for y=5? Wait — actually, looking:

In the image, the gray shape:

- At row y=5: columns x=-3 and x=-2 are filled? Or only x=-3?

Actually, let's count:

From left:

Column x=-5: filled at y=2 and y=3?

Perhaps list coordinates of centers or corners.

Standard way: Assume each grid line is integer, and shapes occupy cells between lines.

So a square at "position (a,b)" means from x=a to a+1, y=b to b+1.

But for translation, we can treat each vertex.

Easier: Pick key points.

For example, the top-right corner of the shape is at approximately (-2,5). Bottom-left at (-5,2).

But let's define the set of points.

From visual inspection:

The shape consists of the following unit squares (using lower-left corner):

- (-5,2)
- (-5,3)
- (-4,2)
- (-3,2)
- (-3,3)
- (-3,4)
- (-2,4)
- (-2,5)

Is that correct? Let's verify:

At x=-5: y=2 and y=3 → two squares stacked.

At x=-4: only y=2? Yes.

At x=-3: y=2,3,4 → three squares.

At x=-2: y=4 and y=5 → two squares.

Total 8 squares? But it looks like 7 or 8.

Anyway, for translation, we apply to each point.

Translate 4 right: add 4 to x

Translate 3 down: subtract 3 from y

So new coordinates:

Original → New

(-5,2) → (-1,-1)

(-5,3) → (-1,0)

(-4,2) → (0,-1)

(-3,2) → (1,-1)

(-3,3) → (1,0)

(-3,4) → (1,1)

(-2,4) → (2,1)

(-2,5) → (2,2)

So the new shape will be drawn with these positions.

Note: Some y-values are negative, which is fine — the grid goes to y=-5.

Now, to confirm, the entire shape moves right 4 and down 3.

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All translations are now calculated.

Final Answer:
For each graph, draw the translated shape as follows:

- Top Left: Triangle moved 4 units right → new vertices at (-1,-4), (1,-4), (0,-3)
- Top Right: Square moved 3 right and 2 down → new corners at (-1,2), (0,2), (0,1), (-1,1)
- Bottom Left: Hexagon moved 3 left → shift all points left by 3; e.g., if original center at (4,2), new at (1,2)
- Bottom Right: Irregular shape moved 4 right and 3 down → each point (x,y) becomes (x+4, y-3); e.g., (-5,2)→(-1,-1), (-2,5)→(2,2), etc.

Students should redraw each shape in its new position on the respective coordinate plane.