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:
$90^\circ$ 9 0 ° , $180^\circ$ 1 8 0 ° , $270^\circ$ 2 7 0 ° and $360^\circ$ 3 6 0 ° 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 $360^\circ$ 3 6 0 ° takes you right back to where you started.
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.
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
Reveal Solution Watch video
Question 2
Which is the correct image after the original is rotated by $45^\circ$ 4 5 ° 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.
Reveal Solution Watch video
Question 3
What is the clockwise angle of rotation of the original image about point $O$ O ?
Reveal Solution Watch video