Grade 8 · Math

8th grade Turn a shape about the origin worksheet

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Turn a shape about the origin

Grade 8 Math Worksheet

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

Triangle CDF on Bo's kite sticker has corners C(1, 2), D(4, 6) and F(5, -1). It turns 90° counterclockwise about the origin. Where is D′? Write it like (7, -3).
Triangle CDF on Esme's sled sticker has corners C(-2, 3), D(-5, -1) and F(1, 4). It turns 90° counterclockwise about the origin. Where is D′? Write it like (7, -3).
Triangle CDF on Jun's plane sticker has corners C(3, -5), D(7, -2) and F(2, 4). It turns 90° counterclockwise about the origin. Where is D′? Write it like (7, -3).
Triangle CDF on Luz's turtle sticker has corners C(-3, 2), D(-6, 4) and F(1, -2). It turns 90° clockwise about the origin. Where is D′? Write it like (7, -3).
Read this first
Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle.
Triangle CDF on Noah's quilt design has corners C(2, 1), D(6, 3) and F(4, -2). It turns 180° about the origin. Where is D′? Write it like (7, -3).
Triangle CDF on Pia's crown design has corners C(-1, 4), D(-5, 2) and F(-3, -6). It turns 180° about the origin. Where is D′? Write it like (7, -3).
Use the picture in question 5.
Triangle CDF on Ren's window design has corners C(1, -2), D(3, -8) and F(6, -4). It turns 180° about the origin. Where is D′? Write it like (7, -3).
Use the picture in question 5.
8.
Zee's snowman design moved on the grid. Corner D went from (4, 1) to (-1, 4), and F went from (2, -3) to (3, 2). Which move was it?
- a turn of 180° about the origin
- a turn of 90° clockwise about the origin of the grid
- a turn of 90° counterclockwise about the origin
- a flip across the y-axis
9.
Ari's rocket design moved on the grid. Corner D went from (3, 5) to (5, -3), and F went from (-2, 1) to (1, 2). Which move was it?
Use the picture in question 8.
- a turn of 90° counterclockwise about the origin
- a turn of 180° about the origin
- a turn of 90° clockwise about the origin
- a flip across the y-axis
10.
Esme's star design moved on the grid. Corner D went from (5, 2) to (-5, -2), and F went from (-1, 3) to (1, -3). Which move was it?
Use the picture in question 8.
- a flip across the x-axis
- a turn of 180° about the origin
- a flip across the y-axis
- a turn of 90° counterclockwise about the origin

8th grade Turn a shape about the origin worksheet – printable — Print: 1 2 3 4 5 6

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.

More grade 8 math

See all grade 8 math

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