Let’s solve each translation problem step by step.
A
translation means sliding a shape without rotating or flipping it. Every point of the shape moves the same distance in the same direction — usually described as “right/left” and “up/down”.
We’ll look at one key point on the original figure (like a corner) and see where it ends up on the translated figure. Then we can describe the whole move.
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Problem 1:
Original triangle has a vertex at (-3, -2).
Translated triangle has that same vertex at (0, -4).
→ From x = -3 to x = 0 → that’s
+3 (move right 3 units)
→ From y = -2 to y = -4 → that’s
-2 (move down 2 units)
✔ Translation:
Right 3, Down 2
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Problem 2:
Pick a clear point — say the top-left vertex of the original quadrilateral: (-3, 5)
In the translated image, that point is now at (3, 2)
→ x: -3 to 3 → +6 (right 6)
→ y: 5 to 2 → -3 (down 3)
✔ Translation:
Right 6, Down 3
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Problem 3:
Take the leftmost point of the original pentagon: (-5, 2)
In the translated version, it’s at (1, -3)
→ x: -5 to 1 → +6 (right 6)
→ y: 2 to -3 → -5 (down 5)
✔ Translation:
Right 6, Down 5
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Problem 4:
Look at the bottom-right corner of the original rectangle: (2, -4)
In the translated image, it’s at (-2, 1)
Wait — let’s double-check with another point to be sure.
Top-left of original: (-3, 3) → becomes (-7, 8)? That doesn’t match.
Actually, let’s pick a better matching pair.
Original square: bottom-right is (2, -4)
Translated square: bottom-right is (-2, 1)
x: 2 → -2 → that’s
-4 (left 4)
y: -4 → 1 → that’s
+5 (up 5)
Check another point: top-left original (-3, 3) → should become (-7, 8)
Yes! In the image, the translated square’s top-left is indeed around (-7, 8).
✔ Translation:
Left 4, Up 5
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Problem 5:
Original trapezoid: bottom-left point at (-4, -5)
Translated: that point is now at (0, -2)
x: -4 → 0 → +4 (right 4)
y: -5 → -2 → +3 (up 3)
✔ Translation:
Right 4, Up 3
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Problem 6:
Original polygon: let’s take the lowest point — approximately (-4, -6)
Translated: that point is now at (0, -3)
x: -4 → 0 → +4 (right 4)
y: -6 → -3 → +3 (up 3)
Wait — check another point to confirm.
Top-right of original: (1, -3) → should become (5, 0)
Looking at the image, yes — the translated shape’s top-right is near (5, 0).
✔ Translation:
Right 4, Up 3
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Final Answer:
1. Right 3, Down 2
2. Right 6, Down 3
3. Right 6, Down 5
4. Left 4, Up 5
5. Right 4, Up 3
6. Right 4, Up 3
Parent Tip: Review the logic above to help your child master the concept of translation in geometry worksheet.
