Lesson video

Hi, I'm Ms. Davis.

In today's lesson, we're going to be applying Pythagoras' theorem to find the the length of a line segment on a coordinate grid.

Here are some questions for you to try.

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Point A has a coordinate of.

Point B has a coordinate of.

Point C has a coordinate of , and point D has a coordinate of.

Make sure you're writing the X coordinate first, as X comes first in the alphabet.

Here are some questions for you to try.

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The distance from point A to point B is five units.

We can see this from counting the number of squares between the points.

From point A to point C is four units, and from point C to point D is three units.

Here are some questions for you to try.

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Here are the answers.

Remember that one subtract negative five is equivalent to one add five.

Also remember that if you square any number it gives a positive solution.

We've been asked to find the distance from point A to point D.

We've already worked out that A to C is four units, And C to D is three units.

I've written these onto the diagram.

This gives us a right-angled triangle.

We can then apply Pythagoras' theorem to this.

The length AD is five units.

We've been asked to find the length of the line segment RS.

This is the distance from point R to point S.

We need a right-angled triangle to apply Pythagoras' theorem to.

This would look like this.

We'd then need to know the length of the shorter side of the triangle.

The X distance, we can see, is four units.

The Y distance is five units.

We can then apply this to Pythagoras' theorem.

Four squared add five squared is the same as 16 add 25, these sum to 41.

Then to find the length of RS we need to calculate the square root of 41.

This is 6.

4, correct to one decimal place.

Here's some questions for you to try.

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Here are the answers.

The length OA and OC is just a case of looking at the X or Y coordinate, whichever isn't zero.

With this question, we've just been given a pair of coordinates, so I'm going to sketch what this would look like.

We need to work out the shorter length of the right-angled triangle.

The X distance would be one, because the distance between two and three is one.

The Y distance would be six, as the difference between four and negative two is six.

We can now apply Pythagoras' theorem.

One squared add six squared can be written as one add 36, which add together to make 37.

To find the value of C, which is our distance between the two coordinates, we need to calculate the square root of 37.

This is 6.

08 to three significant figures.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished, Here are the answers.

In part A we're using the origin, which is the point.

This means that the sides of our right-angled triangle, A and B are are nine and 13.

In part B, we have one point that has coordinates , so that must be point B.

The other point has coordinates , which must be point C.

Again, we've only been given two coordinates.

I'm going to draw a sketch without a grid to show roughly where the coordinates would be in relation to each other.

I can then find the X and Y distances from the coordinates given.

The X distance will be 10, as the difference between nine and negative one is 10.

The Y distance is seven, because the difference between negative three and four is seven.

We can now apply Pythagoras' theorem.

This gives us a solution of 12.

2 to one decimal place.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

You need to find the distance between the coordinates.

For part C, to find the X distance, you could do negative two takeaway four, or four take away negative two.

It doesn't matter which calculation you do, as long as it's consistent for the Y distance.

For example, if you did negative two take away four for the X distance, you need to do zero take away nine for the Y distance.

Here is a question for you to try.

Pause the video to complete your task, and resume once you finished.

To find the Y coordinate of Point A, you will need to substitute three in as X.

This gives a coordinate of.

Coordinate of point B is found by substituting negative four into the equation.

This gives a coordinate of.

You can then find the shorter length of the right-angled triangle, and use Pythagoras' theorem to give AB as 22.

1cm.

That's all for this lesson.

Thanks for watching.