Rotating Around Axis - Rotate Shapes and Find New Coordinates - Angle Rotation Practice

Sep 30, 2026

Uploaded by Asher

Practice sheet for rotating shapes around the origin using a rotation angle. The document provides the rotation formula with cosine and sine terms, defines variables x1 and y1, and works through an example starting from coordinates (1,4) rotated by 60°. It then lists multiple problems requiring students to rotate shapes by specified degrees (e.g., 99°, -40°, -292°, 45°) and report the resulting coordinates, followed by an answer key.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Rotation Formula

Example Rotation (60°)

Practice Problems (99°, -40°, -292°, 45°)

Answers

Rotating Around Axis Name: II I III IV II I III IV II I III IV II I III IV Rotate each shape. Answer with the new coordinates. θ = Angle of Rotation Rotation Formula x1 = x×cos(θ) -y×sin(θ) y1 = x×sin(θ) + y×cos(θ) In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° . 1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60) 2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5 3. x1 = 0.5-3.48 y1 = 0.87 + 2 4. x1 = -2.98 y1 = 2.87 5. Looking at shape, we can see that rotated 60° it is at (-2 .98 , 2 .87) . Answers 1. 2. 3. 4. 1) Rotate the shape 99° around the point (0,0) . 2) Rotate the shape-40° around the point (0,0) . 3) Rotate the shape-292° around the point 4) Rotate the shape 45° around the point (0,0) . (0,0) . [Math](Math www.CommonCoreSheets.com 6 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 6 1-4)[ 6](Math www.CommonCoreSheets.com 6 1-4)[ 1-4](Math www.CommonCoreSheets.com 6 1-4) 75 50 25 0 Rotating Around Axis Name: Answer Key |
Rotate each shape. Answer with the new coordinates.
θ = Angle of Rotation
Rotation Formula
x1 = x×cos(θ) -y×sin(θ)
y1 = x×sin(θ) + y×cos(θ)
In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .

1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)
2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5
3. x1 = 0.5-3.48 y1 = 0.87 + 2
4. x1 = -2.98 y1 = 2.87
5. Looking at shape, we can see that rotated 60° it is at
(-2 .98 , 2 .87) .
| | Answers 1. (6.3,-5)
2. (9.9,-0.9) 3. (5.6,-3.1) 4. (-0.7,2.1) | | --- | --- | --- | | 1) Rotate the shape 99° around the point (0,0) .
(4 - 7) ,
II I
III IV
| 2) Rotate the shape-40° around the point (0,0) .
| | | 3) Rotate the shape-292° around the point 4) Rotate the shape 45° around the point (0,0) . (0,0) .
5,- 4)
II I
III IV

(- 2, -1 )
II I
III IV

| | | [www.CommonCoreSheets.com](www.CommonCoreSheets.com 6 1-4)[ 6](www.CommonCoreSheets.com 6 1-4)[ 1-4](www.CommonCoreSheets.com 6 1-4) 75 50 25 0 Math Rotating Around Axis Name: |
Rotate each shape. Answer with the new coordinates.
θ = Angle of Rotation
Rotation Formula
x1 = x×cos(θ) -y×sin(θ)
y1 = x×sin(θ) + y×cos(θ)
In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .

1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)
2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5
3. x1 = 0.5-3.48 y1 = 0.87 + 2
4. x1 = -2.98 y1 = 2.87
5. Looking at shape, we can see that rotated 60° it is at
(-2 .98 , 2 .87) .
| | Answers
1.
2. | | --- | --- | --- | | 1) Rotate the shape 99° around the point (0,0) .

II I
III IV
| 2) Rotate the shape-40° around the point (0,0) .
| | Math Modified [www.CommonCoreSheets.com](www.CommonCoreSheets.com) 6 1-2 50 0 | | | | --- | --- |

FAQs

What rotation formula does the worksheet use to compute the new coordinates?

It uses x1 = x×cos(θ) − y×sin(θ) and y1 = x×sin(θ) + y×cos(θ) to find the rotated coordinates.

How is the worksheet’s worked example performed for a 60° rotation?

Starting from (1,4), it substitutes θ = 60° into the formula to compute x1 and y1, yielding approximately (-2.98, 2.87).

What do the practice questions ask students to do?

They rotate the given shape by specific angles around the point (0,0) and then provide the new coordinates as the answer.

Sep 30, 2026

Uploaded by Asher