Video: GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 16

GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 16

02:49

Video Transcript

Rotate the trapezium 90 degrees clockwise about the origin on the grid below.

Okay, so we’re being asked to perform a rotation of this trapezium. And let’s just make sure we’re clear about the details of this rotation first. Firstly, the angle that we’re given to rotate this trapezium through is 90 degrees. So as there’re 360 degrees in a full turn, this means we’re rotating the shape through a quarter of a turn.

Secondly, we’re told that the direction of this rotation needs to be clockwise. So for this shape, this means we’re rotating in a sort of downwards direction. Next, we’re told that this rotation is about the origin, which is the point zero, zero. And this means that this is the point, which stays fixed, while everything else moves.

Now, if you have access to a piece of tracing paper, then you could lay the tracing paper over this diagram. You could trace the trapezium onto your tracing paper, put the point of your pencil at the origin, and then rotate your tracing paper through 90 degrees clockwise and draw the image of this trapezium at the point where the tracing paper ends up.

However, if you don’t have access to tracing paper, I’m going to show you another method that you could use. What I’m going to do is drawing some horizontal and vertical lines that connect each corner of our trapezium to the centre of rotation, which is the origin.

So for the first corner, we have these orange dotted lines here. We can then rotate these lines to 90 degrees clockwise. So as this is a quarter turn, that line that was originally vertical along the 𝑦-axis will now be horizontal along the 𝑥-axis. And the line that was horizontal going to the right is now vertical going down. This tells us where that point on the original trapezium will end up once we’ve rotated it.

We can do this for the other corners of the trapezium. So I connect another corner to the centre of rotation and then rotate these lines to 90 degrees clockwise to see where this corner will map to. We can then do the same thing for the third corner of our trapezium and then also the fourth corner.

We can then connect these four points together to show where the trapezium has mapped to. Notice that our rotated trapezium is exactly the same size and shape as the original trapezium. But it’s just in a different position and orientation.

So we’ve successfully rotated the trapezium through 90 degrees clockwise about the origin.

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