Combined Transformations

Lesson

Practice

Lesson

A transformation is a change, so when we transform a shape, we change it in some way. There are three kinds of transformations: reflections, rotations and transformations. Let's recap these first.

Reflection (Flip)

We see reflections all the time- in mirrors, in pools of water and so on. A flip is a reflection over a line or axis. We can see in the picture below that the blue object has been reflected over the vertical axis to create the green image. Notice how they are exactly the same distance from the $y$y-axis?

Rotation (Turn)

A shape is rotated around a centre point in a circular motion. It does not have to be turned in a full circle, otherwise it would be back and the same point. We commonly see $90^\circ$90° turns (also known as quarter turns), $180^\circ$180° turns (half turns) and $270^\circ$270° turns (three-quarter turns). The triangle below has been rotated anticlockwise $90^\circ$90°.

Translation (Slide)

The whole shape moves the same distance in the same direction, without being rotated or flipped. In the picture below, we can see the diamond has been translated (slid) to the right.

After any of those transformations (rotations, reflections and translations), the shape still has the same size, area, angles and line lengths. However, a shape may be transformed in more than one way. Let's look through some examples now.

Examples

Question 1

What two transformations would be needed to get from Flag $A$A to Flag $B$B?

Two flags, flag A and flag B are placed on a square grid. Each flag has a triangular flag, a pole and a base. Both flags have the same shape and size and are oriented upright, with their flags on top. The triangular flag of flag A points to the right, while triangular flag of flag B points to the left. From the upper-left of the grid, the base of flag A is located at the 4th horizontal line, and 2nd vertical line. From the upper-left of the grid, the base of flag B is located at the 2nd horizontal line, and 6th vertical line.

Rotation and translation
A
Two translations
B
Two reflections
C
Reflection and translation
D

Question 2

When the original image is rotated $90^\circ$90° $clockwise$ about point $O$O and then translated $3$3 units $up$ , what is the new image?

$J$J
A
$H$H
B
$N$N
C
$K$K
D

Question 3

A shape is translated, then rotated about its centre.

The same result can always be obtained by a rotation about its centre, followed by a translation.

True or false?

True
A
False
B