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Grade 8 · Math · Unit 12 of 14

Tessellations & Transformations

Slides, flips, turns and dilations

What your child practises

Why some shapes tessellate, naming the transformations in a tiling, and finding the image of a point after a translation, reflection, rotation or dilation on a coordinate grid.

Prince Edward Island Curriculum curriculum outcome: Shape and Space · tessellations and transformations of shapes

How we explain it

Children can open this short lesson before they practise.

  1. A translation slides, a reflection flips, a rotation turns and a dilation resizes.
  2. A tessellation covers a surface with copies of a shape with no gaps.
  3. On a grid, a translation adds to or subtracts from x and y.

Example: Translate (1, 2) right 3 and down 4. Right 3: x = 1 + 3 = 4. Down 4: y = 2 − 4 = −2. Answer: (4, −2)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Point A(3, 6) is rotated 90° counterclockwise about the origin. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (−6, 3)
    • (−3, 6)
    • (3, −6)
    • (−3, −6)

  2. Question 2

    Which rule describes a reflection in the x-axis?

    • (x, y) → (x, −y)
    • (x, y) → (y, x)
    • (x, y) → (−x, y)
    • (x, y) → (−x, −y)

  3. Question 3

    Point A(−2, −4) is reflected in the y-axis. What are the coordinates of A′?

    -9-9-8-8-7-7-6-6-5-5-4-4-3-3-2-2-1-100112233445566778899A
    • (2, 4)
    • (−2, 4)
    • (2, −4)
    • (−4, −2)

  4. Question 4

    In a tiling of triangles, every second triangle is a flipped copy of the one next to it across a shared side. Which transformation links them?

    • reflection
    • translation
    • dilation
    • a slide

  5. Question 5

    Squares tessellate because each angle is 90°. How many squares meet at each point?

    • 8
    • 3
    • 6
    • 4

  6. Question 6

    A rectangle is dilated by a scale factor of 4. A side that was 7 cm long is now how long, in centimetres?

    answer boxcm

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