Lesson video

Welcome to our third lesson in our coordinates and shapes unit.

Today, we'll be learning to reflect shapes.

You will need a pencil and a piece of paper.

Ideally square paper like your maths book, pause the video and get your equipment if you haven't already.

So today, we'll be reflecting simple shapes on a coordinate grid.

We'll start off with a quiz to test your knowledge from the previous lesson.

Then we'll describe reflections before reflecting shapes on a grid.

Then you will do some independent learning to practise what you've been taught and a final quiz to test your knowledge from the whole lesson.

So let's start with our initial knowledge quiz, pause the video and complete the quiz to show what you've remembered from our previous lesson.

Great work.

So we're looking at reflections today.

A shape can be reflected across a line of reflection to create an image.

And the line of reflection is called the mirror line.

Every point on the image is the same distance from the mirror line as the original shape.

And nothing changes about the shape apart from the fact that it has reflected the size stays exactly the same.

And we're going to start off by describing reflections.

So let's have a look, first of all, what shape has been drawn and how do we know? Just looking at the shape, I don't immediately recognise it.

So I'm going to count the sides.

One, two, three, four, five, it has five sides.

So I know it's pentagon and I can see that the sides are different lengths.

Therefore, it's an irregular pentagon.

Now I'm being asked, what are the coordinates of its vertices? So I'm going to write them all here.

So A, I go along the X axis first to minus four and then up the Y axis to eight.

So A is at minus four, eight.

I remember my rule from the top left quadrant is that the X coordinate is negative and the Y is positive.

So let's look at that rule unfold.

B is at minus five, five.

C is at minus four, four.

D is minus two, four and E is minus two, eight.

So yes, they all have a negative X coordinate and a positive Y coordinate.

Now the shape has been reflected and we can see that the pentagon has not changed size at all.

Now, what we said about reflections was that the points will all stay the same distance from the axis.

In this case, the axis is always going to be the mirror line.

And we can see that the mirror line here was the Y axis.

Therefore this shape has been reflected in the Y axis.

You can see that point A was two away from the Y axis before the reflection and after the reflection, it's also two away from the Y axis.

And we can say the same for all of the others.

A was four units away, and it's still four units away, it's just been reflected in the Y axis.

Now the shape has been reflected in the X axis.

The X axis is essentially the mirror line.

So D was one, two, three, four units away from the X axis.

And it is in its reflection, one, two, three, four units away.

So they are the same distance away from the mirror line.

So now we're looking at the reflections.

We're going to have a look at the coordinates.

Let's think about what do we notice about the coordinates? So the first shape, shape A is in the top left quadrant.

I know that the coordinates in the top left quadrant have negative X and positive Y coordinates.

And I can see that in all of these blue coordinates.

I've got minus four, eight.

This one here is the top one, and that is minus four, eight negative X and positive Y.

Now the mirror line here was the X axis.

So this has been reflected in the X axis.

And I can see now that the coordinates in the bottom left quadrant are negative X and negative Y and I can see that in these coordinates.

But if I look at a comparison of the coordinates, then I start to notice something interesting.

So if I take this one, for example, this is the point here on shape A and here on shape B, you can see that the numbers have not changed.

The only thing that has changed here is whether they are negative or positive.

Reason they haven't changed is because they are the same distance away from the axis.

So now, if I had shape a reflected in the top right quadrant, what do you think the coordinates would be? So I that the top right quadrant is positive X and positive Y and I know that the coordinates would stay the same.

So instead of being minus four eight, this coordinate would be four, eight.

And instead of being minus two, eight, this would be two, eight because the distance from the axis doesn't change.

Now, what about if we had this one, think about this.

Reflected in the Y axis, what would the coordinates be? What do you know about the bottom right quadrant? So we know that the bottom right quadrant is positive X, negative Y.

So we know that these coordinates here, the numbers would stay exactly the same, but the coordinates would change to have a positive X.

So for example, this one would be a four and a negative Y minus four.

So four minus, four.

Now let's think about reflecting shapes.

So I want to reflect the rectangle in the X axis.

I know that the X axis is going to be my mirror line.

So the shape is going to end up in the bottom right quadrant.

So I'm going to show you how to reflect the shape.

I'm going to start with the.

Remember that it needs to be the same distance from the axis as we're reflecting.

So currently it's one to three units from the X axis.

So I need to go three below the X axis.

And this is where my B is now.

C was also three.

So C is going to be here.

D was one, two, three, four, five.

So it's going to be one, two, three, four, five.

So that's going to be here.

And then I can see looking at it as a rectangle, that A is going to be here.

Now I'll check it by looking at the coordinate.

So I'm going to go with C.

So in its original position, C was at six, three.

Remember the coordinates for the same point, shouldn't change it's only whether it's positive or negative.

So C in the post reflection shape is at six, minus three.

And we know that the bottom right quadrant has a positive X and a negative Y, and we check it with one other one, A went from being three, five, and we can already predict that because it's going to be positive X and negative Y.

It should be three minus five, three minus five.

That's correct.

Now we're going to reflect it in the Y axis.

So the Y is going to be our mirror line, and we're going to do exactly the same thing, reflect each vertex.

So that A was one, two, three from the Y axis.

So we do it one, two, three the other side, and that's A, we know it's the same for B and D.

And when to do it up here is one, two, three, four, five, six from the Y axis.

One, two, three, four, five, six other on puts it here.

So that's D and C is below.

And I can just check that they are both two units in length they are, and three units wide.

And that's correct.

Now, it's your turn, pause the video and reflect the shapes.

So you're going to reflect the triangle in the X axis, and you're going to reflect the trapeziums in the Y axis.

So your triangle was reflected in the X axis, which means that it was going to end up in the bottom left quadrant.

Point B and C were both two from the X axis.

So we go two down here and we can see that they're going to be here and here.

And A was one, two, three, four, five away.

One, two, three, four, five, and that we can label it as well.

And we can check that they're the same width and the same height as they were originally.

And then you can also show the comparison between the coordinates.

I'll just do it for B.

So in the original one, it was minus eight, two, which is negative X and positive Y and then this one is going to be negative X negative Y.

So B is minus eight minus two.

And then you were reflecting the trapezium in the Y axis.

So the Y was your mirror line.

So you could see D was one unit away from the Y axis.

So one unit to here, same with C and then A was four units.

And then the same with B.

And then just check that you've got the correct height for each of those points there.

I think you're ready for some independent learning.

So pause the video and complete the task.

And once you're finished, press restart so that we can go through the answers together.

Now in question one, you had a statement to disagree with.

So it says that, the blue triangle has been reflected in the X axis.

Give two reasons why that statement is incorrect.

Well, the first reason is that if it had been reflected in the X axis with the X being the mirror line, then it would have ended up in the bottom left quadrant, but it suggests that it reflected in the Y axis because it's ended up in the opposite quadrant in the top right.

So if it's been reflected at all, it's been reflected in the Y axis, but actually we can argue that it hasn't been reflected at all, because although it is the same distance from the Y axis, the shape has not stayed the same size.

And when we're reflecting, we are not changing the size of the shape.

In question two you were asked to reflect the kite in the X axis and then write the coordinates of its new vertices.

So the X was your mirror line.

So C was one away, so that would go there.

C and that coordinates of C are five, minus one, B is one, two, three, four away from the X axis.

One, two, three, four takes us to here.

So that will be B.

And B is that four, minus four, A is one, two, three, four, five, six from the X axis, one, two, three, four, five, six.

That's A, and A is now at five minus, six.

And D is four from the axis.

And it's also two across B.

And the coordinates for D are six minus four.

And you may have used a ruler to join those vertices together so that you can see the shape reflected.

Now you have to reflect the trapezium in the X axis.

So the X was your mirror line.

So D was four away.

So you went for further up and D is there.

C was one, two, three, four, five, six, seven, eight away.

So you went four, five, six, seven, eight.

So that's C and then we can see that the width of the shape is three units.

So we know that these A and B are going to be on this line somewhere.

A was one, two, three, four, five units from the mirror line one, two, three, four, five, and B was too far.

They were seven.

So B is there.

And then you were also asked to write the coordinates of the new vertices.

So I'll start with A minus four, five.

And we know that these should all have a negative X coordinate and a positive Y coordinate.

B was minus four, seven.

C was at minus one, eight.

And D was at minus one, four.

Question four, you were asked to reflect the pentagon in the Y axis.

So this is our mirror line here.

I'll start with D one, two, three away.

One, two, three, so D is here.

And then you may have first tried to recreate the shape in the flipped, in the reflected orientation.

By saying that E is two across and one higher, or you may have just shown D, done you're counting across from the axis.

So E is one, two, three, four, five from the Y axis one, two, three, four, five.

So E is here.

And you can see also that that is, like I said, there it's two across and one up.

So you can see the patterns there.

A is in line with D one, two, three, four, five, six, seven, eight from the axis three, four, five, six, seven, eight.

So A is here, and then I can look at C and count is four away, so it's going to be here.

And then the last one B I know that that is three further along, put my C in there X works better.

And then B sorry is three further along from C.

So B is going to end up here.

And again, you were asked to write the new coordinates of your vertices so A is eight, seven.

B is seven, five.

And these are all positive coordinates.

C is four, five.

D is three, seven.

And E is five, eight.

It's really helpful to remember those quadrant rules, because then I can see that I haven't made any silly mistakes with my reflecting.

And then question five was slightly trickier where you weren't given any numbers on your axis, but this is why we have learned some simple rules about reflecting coordinates.

Triangle B is a reflection of triangle A.

First of all, which axis was it reflected in? I can see that this is the mirror line reflected in the Y axis.

And then my second question is what are the coordinates of triangle B? So these two sets of coordinates are in the bottom left quadrant.

And I remember the bottom left is negative Y.

Oh, why am I doing that that way around? Negative X, negative Y.

And remember the coordinates don't change, the numbers don't change.

So it is just whether they are positive or negative.

So two, three is going to become two, minus three and six minus, three is going to become minus six, minus three.

And it's important that you reflected them and you didn't write two, minus three here and six, minus three here, because that would probably then have been a translation.

And then in the top left quadrant, we have negative X and positive Y.

So four, three is going to become minus four, three.

Great work, pause the video and complete your final quiz to test everything you've learned today.

You've done an excellent job today.

I'll see you in our next lesson where we'll be solving, coordinate problems, see you then.