Transformations on a grid · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Transformations on a grid

Mathematics · Geometry · ages 9-12
Name ______________________   Date ____________

  1. A shape moves 4 squares right and 1 square up. A corner starts at (1, 1). What is the x-coordinate of the corner after the move?

    Answer: ______________

  2. A point at (2, 3) is reflected in the vertical mirror line x = 0. Where does it land?

    • (-2, 3)
    • (2, -3)
    • (3, 2)
    • (-3, -2)

  3. Which move flips a shape over a line, making a mirror image?

    • Reflection
    • Translation
    • Rotation

  4. True or false: after you rotate a shape 90 degrees about a centre point, the image is still exactly the same size as the original.

    Circle one:   True   False

  5. A shape is rotated 180 degrees about the origin. A corner at (3, 1) moves to which point?

    • (3, -1)
    • (-3, 1)
    • (-3, -1)
    • (1, 3)

  6. A point at (6, 1) is reflected in the vertical line x = 4. What is the x-coordinate of the image?

    Answer: ______________

  7. A triangle is translated 3 squares left and 2 squares down. A vertex at (5, 6) moves to which point?

    • (8, 8)
    • (2, 8)
    • (2, 4)
    • (8, 4)

  8. A point at (4, 0) is rotated 180 degrees about the centre (0, 0). Where does the image land?

    • (-4, 0)
    • (0, 4)
    • (4, 0)

  9. A shape is reflected in a diagonal mirror line drawn corner to corner across the grid. Which statement is correct?

    • Diagonal lines cannot be used as mirror lines for reflections
    • You still measure the mirror distance straight across the line, just like any other mirror line
    • The image will look like a completely different, bigger shape

  10. A point at (7, 1) is reflected in the vertical line x = 5. 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.

Transformations on a grid W1-mt_SH7QgFl8-v-s1

  1. 5 · 1 + 4 = 5.
  2. (-2, 3) · A vertical mirror flips the x sign: (2, 3) lands on (-2, 3).
  3. Reflection · A reflection flips a shape over a mirror line, so the image is a mirror copy of the original.
  4. True · Rotating never stretches or shrinks a shape. It only turns it, so the image stays congruent to the original.
  5. (-3, -1) · A half turn about the origin flips both signs: (-3, -1).
  6. 2 · 6 is 2 right of x = 4, so the image is 2 left of it: x = 2.
  7. (2, 4) · (5 - 3, 6 - 2) = (2, 4).
  8. (-4, 0) · A 180-degree rotation about the centre sends every point to the exact opposite side, so (4, 0) becomes (-4, 0).
  9. You still measure the mirror distance straight across the line, just like any other mirror line · Any straight line can be a mirror line, including diagonals. Each point of the image sits the same distance from the line as its matching point on the original.
  10. 3 · 7 is 2 right of x = 5, so the image is at 5 - 2 = 3.
Worksheet · LightMySky