Video Transcript
Does the following figure have
rotational symmetry? If yes, find the angle of
rotation.
In order to answer this question,
let’s recall what we mean by the order of rotational symmetry. The order of rotational symmetry of
a geometric figure is the number of times you can rotate the figure so it still
looks the same as the original figure. And that’s within a 360-degree
rotation. So let’s consider the figure that
we’re given. It is in fact a square, as both the
length and the width would be the same length. If we count the squares along both
sides, then each of these would be six squares long.
When we’re working out rotational
symmetry, we’ll need to consider any picture or pattern on the figure. This figure would in fact have two
lines of symmetry along the diagonals. And while we’re not thinking about
lines of symmetry, this will help us when we’re rotating. If we rotate this square through 90
degrees, the lengths would fit along like the original shape, but the patterns
wouldn’t match. This white square, for example, can
sit on a black square and still look the same as the original image.
So let’s instead think about a
180-degree rotation of the original shape. We would now have a white square on
top of a white square and black squares on top of black squares. Therefore, after a rotation of 180
degrees, the rotated image would look the same as the original shape. This would happen again after a
complete rotation of 360 degrees. Because the shape looks the same as
the original figure once after a rotation of 180 degrees and then for a second time
at 360 degrees, we say that the order of rotational symmetry is two. Any shape that has an order of
rotational symmetry more than one has got rotational symmetry. This means that our answer would be
yes.
So next, we need to find the angle
of rotation. The angle of rotation is the
smallest angle for which the figure can be rotated to coincide with itself. It can be calculated using the
formula that the angle of rotation is equal to 360 degrees divided by the order of
rotational symmetry. So we need to divide 360 degrees by
two, giving us a value of 180 degrees. We can therefore give our answer
that yes, this figure has rotational symmetry and the angle of rotation is 180
degrees.
