Rotations I

Lesson

Practice

Lesson

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 spun around (like going in a circle). Every point on the original shape has a matching point on the new shape.

Commonly we describe rotations using a degree measure (like an angle), and as being either clockwise or anticlockwise.

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

$90^\circ$90° (a quarter turn), $180^\circ$180° (a half turn), $270^\circ$270° (a three-quarter turn) and $360^\circ$360° (a full turn) 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

Examples

Question 1

Which picture shows a rotation?

Think: Which one looks like it has been spun around?

Do:

C has been translated (slid) into a different position.

B looks like a mirror image of the original. So this is a reflection (flip).

A has been spun around $180^\circ$180°. This is the rotation!

Question 2

Select all the rotations.

A
B
C
D

QUESTION 3

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

QUESTION 4

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.

$B$B
A
$M$M
B
$H$H
C
$A$A
D