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Position and Transformation
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Rotations II

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Lesson

Rotation

A rotation is what occurs when we turn an object or shape around a central point.  The object is exactly the same shape and size, just rotated around (like going in a circle). Every point on the object or shape has a corresponding point on the image. 

Commonly we describe rotations using a degree measure, and as being either clockwise or anticlockwise.

Particularly at the moment you need to be able to identify rotations of:

$90^\circ$90°, $180^\circ$180°, $270^\circ$270° and $360^\circ$360° in both clockwise and anticlockwise directions.  

Have a play with this interactive. Here you can change the shape that of the object and the position of the central rotation point. Notice how a rotation of $360^\circ$360° takes you right back to where you started.

Created with Geogebra

 

Here are some worked examples.

Question 1

Which of the following figures represents the given flag after rotating it anticlockwise around the red point by 90° ?

A square grey flag with a flag pole on a grid plane is depicted. It is represented by a square with a vertical line segment extending from its right side 1 unit downward, representing the flagpole. The end of the flagpole has a red point indicating its center of rotation.
  1. A square grey flag with a flag pole on a grid plane is depicted. It is represented by a square with a horizontal line segment extending from its top side 1 unit to the right, representing the flagpole. The end of the flagpole has a red point indicating its center of rotation.
    A
    A square grey flag with a flag pole on a grid plane is depicted. It is represented by a square with a vertical line segment extending from its left side 1 unit upward, representing the flagpole. The end of the flagpole has a red point indicating its center of rotation.
    B
    A square grey flag with a flag pole on a grid plane is depicted. It is represented by a square with a horizontal line segment extending from its bottom side 1 unit to the left, representing the flagpole. The end of the flagpole has a red point indicating its center of rotation.
    C
    A rectangle grey flag with a flag pole on a grid plane is depicted. It is represented by two squares stacked vertically with a vertical line segment extending from its right side 1 unit downward, representing the flagpole. The end of the flagpole has a red point indicating its center of rotation.
    D

 

Question 2

Which is the correct image after the original is rotated by $45^\circ$45° clockwise?

Five triangles are shown on a grid labeled "ORIGINAL", "A", "M", "H", and "B", and shaded in red, green, blue, purple and yellow respectively. A point labeled "central point" is shown indicating a pivot point. "A", "M", "H", and "B" are rotation of "ORIGINAL". The ORIGINAL triangle has a horizontal longest side at the bottom and has an opposite vertex at the top. Triangle A has a slanted longest side and the opposite vertex and another vertex are horizontally aligned to the central point. Triangle M has a vertical longest side and has an opposite vertex at the right. Triangle H has a horizontal longest side at the top and has an opposite vertex at the bottom. Triangle B has a vertical longest side and has an opposite vertex at the left. The original triangle is positioned on the upper right of the central point.

  1. $B$B

    A

    $M$M

    B

    $H$H

    C

    $A$A

    D

 

Question 3

What is the clockwise angle of rotation of the original image about point $O$O?

  1. $\editable{}$°

 

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