Translation Worksheets - Free Printable

Looking at the worksheet, the task is to write a rule for each translation shown on the coordinate grids.

A translation moves every point of a shape by the same distance in the same direction. We describe this using a rule like (x + a, y + b), where:
- a is how many units we move left or right (positive = right, negative = left)
- b is how many units we move up or down (positive = up, negative = down)

Let’s go through each one:

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Problem 1:
Original triangle has points at approximately:
- A(-3, 2), B(-1, 2), C(-2, 0)
Translated triangle has points at:
- A'(-3, -2), B'(-1, -2), C'(-2, -4)

Compare:
- x stays same → no horizontal movement
- y goes from 2 to -2 → that’s down 4 units
So rule: (x, y - 4)

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Problem 2:
Original quadrilateral:
- A(-2, 3), B(0, 3), C(1, 1), D(-1, 1)
Translated:
- A'(0, 5), B'(2, 5), C'(3, 3), D'(1, 3)

Compare:
- x: -2 → 0 → +2
- y: 3 → 5 → +2
Rule: (x + 2, y + 2)

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Problem 3:
Original triangle:
- A(-2, 1), B(2, 1), C(0, -1)
Translated:
- A'(-2, -2), B'(2, -2), C'(0, -4)

Compare:
- x stays same
- y: 1 → -2 → down 3
Rule: (x, y - 3)

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Problem 4:
Original triangle:
- A(-1, 1), B(1, 1), C(0, -1)
Translated:
- A'(-1, -2), B'(1, -2), C'(0, -4)

Compare:
- x stays same
- y: 1 → -2 → down 3
Rule: (x, y - 3)

Wait — let me double-check Problem 4.

Actually, looking again:

Original: A(-1,1), B(1,1), C(0,-1)
Translated: A'(-1,-2), B'(1,-2), C'(0,-4)

Yes, y decreased by 3 for all points. So yes, (x, y - 3)

But wait — Problem 3 and 4 are identical? Let me check the image again.

Actually, in Problem 4, the original triangle is higher up? No — looking carefully:

In Problem 4, original triangle has base at y=1, tip at y=-1. Translated has base at y=-2, tip at y=-4. So yes, down 3.

But let’s check Problem 5.

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Problem 5:
Original triangle:
- A(-3, 1), B(-1, 1), C(-2, -1)
Translated:
- A'(-1, -1), B'(1, -1), C'(0, -3)

Compare:
- x: -3 → -1 → +2
- y: 1 → -1 → -2
Rule: (x + 2, y - 2)

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Problem 6:
Original triangle:
- A(-1, 3), B(1, 3), C(0, 1)
Translated:
- A'(-2, 0), B'(0, 0), C'(-1, -2)

Compare:
- x: -1 → -2 → -1
- y: 3 → 0 → -3
Rule: (x - 1, y - 3)

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Now let’s compile all answers:

1. (x, y - 4)
2. (x + 2, y + 2)
3. (x, y - 3)
4. (x, y - 3)
5. (x + 2, y - 2)
6. (x - 1, y - 3)

Wait — Problem 3 and 4 both say (x, y - 3)? That seems odd. Let me recheck Problem 4.

Looking at Problem 4 again:

Original triangle: vertices at (-1,1), (1,1), (0,-1)
Translated triangle: vertices at (-1,-2), (1,-2), (0,-4)

From y=1 to y=-2 is -3. From y=-1 to y=-4 is also -3. Yes, correct.

But maybe the original figure in Problem 4 is different? Actually, looking at the image description, perhaps I misread.

Alternatively, maybe Problem 4 is meant to be different. But based on coordinates, it’s consistent.

Perhaps the worksheet has two similar problems. That’s possible.

Final verification:

All translations are rigid moves — same shape, just moved.

Rules are based on comparing corresponding points.

I think my answers are correct.

Final Answer:
1. (x, y - 4)
2. (x + 2, y + 2)
3. (x, y - 3)
4. (x, y - 3)
5. (x + 2, y - 2)
6. (x - 1, y - 3)