Reflection and Translation on a Grid · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reflection and Translation on a Grid

Mathematics · Geometry · ages 9-10
Name ______________________   Date ____________

  1. A shape moves 3 units right and 2 units up. A corner at (1, 0) ends at which x-coordinate?

    Answer: ______________

  2. A triangle vertex at (1, 4) is reflected in the vertical line x = 3. Where does it land?

    • (5, 4)
    • (1, 2)
    • (3, 4)
    • (1, 6)

  3. When you reflect a shape in a vertical mirror line, what happens to the y-coordinate of each point?

    • It stays the same
    • It changes sign
    • It becomes zero

  4. A shape and its reflection are congruent, meaning they are exactly the same size and shape.

    Circle one:   True   False

  5. A vertex at (4, 5) is reflected in the vertical line x = 3. What is the x-coordinate of the image?

    Answer: ______________

  6. Which of these stays true after you translate a shape across the grid?

    • The shape becomes a different size
    • The shape stays exactly the same size and shape
    • The shape's angles change

  7. A shape is translated 3 right and 2 up. A corner at (4, 1) moves to which point?

    • (7, 3)
    • (1, 3)
    • (4, 3)
    • (7, -1)

  8. Harry describes a move as 3 units right and 2 units up. His friend moves 2 up then 3 right. Will the friend land in the same place?

    Circle one:   True   False

  9. Ben reflects a square in a vertical mirror line and says the new square is bigger because it moved further from the mirror line. Is he correct?

    • No, reflecting only changes position, never size
    • Yes, points further from the mirror line get bigger
    • Only if the square starts on the mirror line

  10. A vertex at (8, 1) is reflected in the vertical line x = 6. What is the x-coordinate of the image?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reflection and Translation on a Grid W1-mt_efOeaGFyGM-s1

  1. 4 · 1 + 3 = 4.
  2. (5, 4) · 1 is 2 left of x = 3, so the image is 2 right: (5, 4).
  3. It stays the same · A vertical mirror line flips left and right, so only the x-coordinate changes. The y-coordinate never moves.
  4. True · A reflection only flips a shape's position. It never changes the size or the angles.
  5. 2 · 4 is 1 right of x = 3, so the image is 1 left: x = 2.
  6. The shape stays exactly the same size and shape · Sliding a shape only moves it. It never stretches, shrinks, or bends the shape.
  7. (7, 3) · (4 + 3, 1 + 2) = (7, 3).
  8. True · Yes: translation order makes no difference.
  9. No, reflecting only changes position, never size · Distance from the mirror line changes where a point lands, not its size. Every reflected shape stays congruent to the original.
  10. 4 · 8 is 2 right of x = 6, so the image is at 6 - 2 = 4.
Worksheet · LightMySky