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Grade 8 · Math

8th grade Turn a shape about the origin worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Turn a shape about the origin

Grade 8 Math Worksheet - Building Confidence

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Circle the best answer, or write your answer on the line.

  1. Read this first

    Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The rocket sticker with corner C(2, 5) marked and a curved arrow 90° counterclockwise about the origin; the image is not drawn.

  2. Ari turns a rocket sticker 90° counterclockwise about the origin. The rule is (x, y) → (−y, x). Corner C is at (2, 5). Where is C′? Write it like (7, -3).

  3. Bo turns a kite sticker 90° counterclockwise about the origin. The rule is (x, y) → (−y, x). Corner D is at (4, -3). Where is D′? Write it like (7, -3).

  4. Esme turns a boat sticker 90° clockwise about the origin. The rule is (x, y) → (y, −x). Corner F is at (3, 6). Where is F′? Write it like (7, -3).

  5. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The butterfly sticker with corner H(-1, -6) marked and a curved arrow 90° counterclockwise about the origin; the image is not drawn.

  6. Kira turns a butterfly sticker 90° counterclockwise about the origin. The rule is (x, y) → (−y, x). Corner H is at (-1, -6). Where is H′? Write it like (7, -3).

  7. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The leaf design with corner Q(3, 7) marked and a curved arrow 180° about the origin; the image is not drawn.

  8. Luz gives a leaf design a half turn (180°) about the origin. The rule is (x, y) → (−x, −y). Corner Q is at (3, 7). Where is Q′? Write it like (7, -3).

  9. Milo gives a rain umbrella design a half turn (180°) about the origin. The rule is (x, y) → (−x, −y). Corner S is at (-2, 6). Where is S′? Write it like (7, -3).

  10. The snowflake design; the image is not drawn. Noah gives a snowflake design a half turn (180°) about the origin. The rule is (x, y) → (−x, −y). Corner U is at (5, -1). Where is U′? Write it like (7, -3).

  11. Ren turns a robot picture 90° counterclockwise about the origin. The table shows corners C and D done. Corner G is at (5, -2). Where is G′? Write it like (7, -3).

  12. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. The bus picture is drawn; the image is not drawn. Table old (x, y) | new (x, y): C(-1, 2) | C'(-2, -1); D(3, 4) | D'(-4, 3); G(6, 1) | ?

  13. Zee turns a bus picture 90° counterclockwise about the origin. The table shows corners C and D done. Corner G is at (6, 1). Where is G′? Write it like (7, -3).

  14. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The tent picture is drawn; the image is not drawn. Table old (x, y) | new (x, y): C(1, -3) | C′(-3, -1); D(2, 4) | D′(4, -2); G(-3, -5) | ?

  15. Ari turns a tent picture 90° clockwise about the origin. The table shows corners C and D done. Corner G is at (-3, -5). Where is G′? Write it like (7, -3).

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8th grade Turn a shape about the origin worksheet – printable
Print: 123456

About this worksheet

Turn a shape about the origin. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can turn a point 90° clockwise or counterclockwise about the origin by swapping its numbers and changing one sign.
  • I can give a shape a half turn (180°) by changing both signs, and say that a 360° turn puts every point back.
  • I can name a turn from a shape and its image, undo a turn, and do a turn and a slide in the order given.

Standard: 8.G.A.3 (rotations)

Words to know

rotation (turn): Turning a shape around a fixed point; here always the origin, (0, 0).

counterclockwise / clockwise: The turn direction: against the hands of a clock, or with them.

quarter turn: A turn of 90°. Two make a half turn; four make a full turn.

half turn: A turn of 180°. Either direction lands in the same place.

image: The shape after the turn. Its corners get a prime mark: D becomes D′.

rule: How every point changes, written (x, y) → (−y, x).

Common mistakes

Your child turned the shape the opposite way, clockwise instead of counterclockwise or the other way round. Turn a book a quarter turn together, both ways, and compare.

Your child swapped the two numbers of the point but forgot that a quarter turn also changes one sign.

Your child changed a sign but kept the two numbers in place, which is a flip, not a turn.

What to say

Ask: after a quarter turn, which number gets the opposite sign?

Ask: after a quarter turn, does the across number stay first?

Questions parents ask

What is the most common mistake with turn a shape about the origin?

Your child turned the shape the opposite way, clockwise instead of counterclockwise or the other way round. Turn a book a quarter turn together, both ways, and compare.

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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