Lesson video

Hello, I'm Miss Miah, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

In this lesson, you'll be using your understanding of properties of polygons to plot missing coordinates in the first quadrant.

Your keywords are on the screen now, and I'd like you to repeat them after me.

Vertex.

Vertices.

Fantastic.

Let's find out what these words mean.

Now, a vertex is the point where two lines meet.

The plural is vertices.

This lesson is all about completing polygons with missing coordinates, and this lesson is made of two lesson cycles.

The first lesson cycle is to do with identifying and plotting missing coordinates.

We then move on to investigating missing coordinates.

Hmm, have you ever worked on a puzzle and been just one piece away from completing it? That piece is super important, right? So today we're going to solve a puzzle just like that.

We'll use our detective skills to find the missing point and complete the polygon.

It's like being a puzzle master, but with polygons.

Ready to find that missing piece? Let's get started.

So to help us in this lesson, we will meet Jacob and Sofia.

So today we will be drawing polygons by plotting their coordinates in the first quadrant of the grid.

Now, it's useful to remember that the first number in a pair x,y is the x coordinate, which tells us how far to move horizontally from the origin.

Yes, and the second number is the y coordinate, which tells us how far to move vertically.

Jacob wants to find the coordinates of the missing vertex to complete the square.

What advice would you give Jacob? You know all sides of a square are equal.

The distances between adjacent points must be the same.

You also know that opposite sides of a square are parallel.

So if AB is one side, CD must be parallel to AB.

So here we can see the parallel sides.

Since AB is equal to BC, the distance from C to D will be the same as from A to B or B to C.

Hmm, I think it's getting a little bit easier for us to identify where that missing point might be.

Jacob says, "By measuring the length of AB, or BC, since they are equal, that's three squares.

From point C, mark this same length along the perpendicular line.

This new point is point D." We've found the missing point to our polygon.

It's created a square.

Jacob has found the missing vertex to complete the square.

He has plotted D.

What advice would you give to Jacob? Hmm, something doesn't look quite right.

Well, you know all sides of a square must have an equal distance.

The distances between the adjacent points must be the same.

You also know that the opposite sides of a square are parallel.

So if AB is one side, CD must be parallel, but they are not.

And you can see that clearly here now.

I can see AB is equal to BC.

The distances from AD and CD, however, are not the same.

So by measuring the length of AB, or BC, since they are equal, that's two squares.

From point C, mark the same along the perpendicular line.

This is now the new point.

So that's where D should be.

Over to you.

You have three vertices of a square: A, B, and C.

Where should point D be? Is it a, somewhere in the middle of the square, b, the same distance from C as A is from B, c, right next to point C, or d, anywhere you want? You can pause the video here and click play when you're ready to rejoin us.

So what did you get? Well, if you got b, you are correct.

You can remember that the vertices of a square are the same distance apart.

Let's move on.

Sofia wants to find the coordinates of the missing vertex to complete the rectangle.

Keyword there.

What advice would you give Sofia? So we've got three points here.

We've got A, B, and C that are plotted already.

We need to find that missing vertex.

Well, you know that rectangles have opposite sides that are equal in length and parallel.

I can see the vertical side AB is parallel to the line that will be formed for CD.

The horizontal side BC is parallel to the line that will be formed to AD.

So sometimes drawing in the parallel line makes it easier for us to visualise where the missing point might be.

Remember the opposite sides are parallel and equal in length.

The distance between two parallel lines is consistent along their length.

We're going to measure the length of side AB.

That's four squares.

From point C, we're going to mark four squares parallel to AB.

This new point will be the fourth vertex, point D.

So let's do that now.

There we go.

Moving on.

Sofia has found the missing vertex to complete the rectangle.

She has plotted D.

What advice might you give to Sofia? Hmm? It doesn't look like a rectangle.

The lines are not parallel.

I can use distance between the vertical lines and horizontal lines to help me.

So the vertical distance between AB is two squares and the horizontal distance between BC is three squares.

Since the distance between the vertical lines is two squares, point D must be aligned two squares down from point C.

That's 4,3.

And that's where the point should be plotted.

The key point here is to remember what the properties of the polygon is that you're working with to help you identify that missing point.

Back to you.

Sofia has plotted three vertices of a quadrilateral.

She thinks that it's a rectangle.

Is Sofia correct? How might she plot C and D differently? You can pause the video here, have a think.

You can also draw the different points onto your grid.

Once you're ready, click play to rejoin us.

So how did you do? Well, Sofia is correct because a square is a regular rectangle.

A rectangle has opposite sides that are equal, but adjacent.

Sides can be different lengths.

You can adjust point C and D like this.

So you could put those points, there, or there, or even there as long as the sides remain adjacent and the polygon itself has two parallel lines and four right angles.

Onto the main task for this lesson cycle.

So for question one, three vertices of a rectangle have been plotted on a coordinate grid.

You're going to plot the fourth vertex.

What are its coordinates? What do you notice about the rectangle? Question two, three vertices of a rectangle have the coordinates 1,1, 1,5 and 5,5.

You're going to find the coordinates of the fourth vertex of the rectangle.

Is it possible to work this out without drawing on a grid? Explain your answer.

You can pause the video here and click play when you're ready to rejoin us.

Off you go.

Good luck.

So how did you do? So for question one, the final coordinate was 5,1, and this completes a square with equal size of four units and four right angles.

Sides are parallel and perpendicular.

This rectangle is a square.

Now for question two, yes, it is possible.

So rectangles have opposite sides that are equal and parallel.

Point D must align with point A horizontally and C vertically.

So this is where you should have plotted point D.

Well done if you've managed to get those two questions correct.

Now let's move on to our second lesson cycle, and that is to investigate missing coordinates.

Now, Sofia plots three vertices of a square on a coordinate grid.

She needs to plot one more point.

Hmm, I wonder if there are some parts of the grid where the point could not go.

Point D would not be the vertex of a square.

The sides would not form pairs of perpendicular sides.

Sofia uses the properties of a square to find the missing coordinate for the vertex.

The final vertex can only be at 8,1 to create a square.

Now Sofia plots four vertices of a pentagon on a coordinate grid.

She needs to plot one more point.

"Hmm, where could the coordinates of the fifth vertex be?" Sofia asks.

A pentagon is a polygon with five sides and five vertices.

There are lots of options when the polygon doesn't have specific properties.

I could plot the last vertex at 7,2.

I have made a pentagon.

If the final vertex was at 10,10, the pentagon would look very different.

Let's have a look.

It's still a pentagon.

Over to you.

Plot one more vertex to make a pentagon with one pair of perpendicular sides.

Remember if sides are perpendicular, they meet at a right angle.

You can pause the video here and click play when you're ready to rejoin us.

So how did you do? So this is where you should have plotted that point.

And I can see that the points meet at a right angle.

You may have also plotted the point here.

And again it's correct because I can see that that final point forms perpendicular sides.

Let's move on.

Jacob plots two vertices of a rectangle.

What could my coordinates of the other two vertices be? Now remember, a rectangle has opposite sides that are equal in length and parallel.

The sides are perpendicular to each other, meaning they meet at right angles.

To find the coordinates, we can move horizontally left or right from A and B.

There are a few different coordinates I could use to position the missing vertices.

Here are some examples.

You could position the points here.

It's still a rectangle.

You could position it here.

And again, it's still a rectangle because the opposite sides are equal and parallel.

And here as well, or here.

Over to you.

Jacob completes a rectangle by plotting points C and D.

Is he correct? You can pause the video here and click play when you're ready to rejoin us.

So how did you do? Jacob is incorrect.

Rectangles have four pairs of perpendicular sides.

Jacob, on the other hand, has made a parallelogram.

Onto the main task for this lesson cycle.

So for question one, Sofia plots three vertices of a square on a coordinate grid.

One a, you're going to plot the fourth vertex and label it with the coordinates.

One b, explain why the vertex has to be at this point and cannot be anywhere else.

Question two, two points of a rectangle are plotted on the coordinate grid.

What could the coordinates of the other two vertices be? Find three possible responses, mark them, and list the coordinates.

Question three, create three different quadrilaterals where one vertex is at point A.

What do you notice? You could pause the video here.

Off you go.

Good luck and click play when you're ready to rejoin us.

So how did you do.

For one a, you should have got 9,2.

A square has four vertices.

The vertices are right angles, so there are four pairs of perpendicular sides.

Position D is the only point where this would be true.

For question two, here are some examples.

So you may have plotted your vertices here.

So C may have been 3,6 and D could have been 8,6.

E and F at 3,0 and 8,0.

G and H at 3,10 and 8,10.

And there may have been other examples as well, as long as it has four straight sides, opposite sides are equal, there are four interior right angles at 90 degrees, and there are parallel sides, meaning the opposite sides are parallel to each other.

So as long as you have these properties, your rectangle is correct.

The points plotted formed a rectangle.

Now for question three, here are some examples.

You may have drawn this, or this, or this.

So if you drew rectangles, some vertices will have shared x or y coordinates of point A.

You could have drawn lots of different quadrilaterals all with four vertices.

Fantastic, we've made it to the end of the lesson.

I really hope you enjoyed it.

Let's summarise our learning.

So today you were completing polygons with missing coordinates.

You should now be able to use your knowledge of polygon properties to identify a missing vertex.

You should also know how to use known coordinates to plot a missing coordinate.

I really hope you enjoyed this lesson, and that you can now see that by knowing the properties of polygons you can figure out what the missing coordinate might be.

Thank you so much for joining me, and I look forward to seeing you in the next lesson.

Bye.