Lesson video

Hi, I'm Miss Davis.

In this lesson, we're going to be looking at vector diagrams that involve midpoints.

Shape A B C D is a parallelogram.

The point M is the midpoint of CD.

We're going to write the vector DC in terms of a and b, DC is parallel and the same length as AB, So it is 8a.

DM is 1/2 of DC, this means that it is 4a, as four is 1/2 of eight.

AM, we're going to start at point A, to travel to point B, to C and then to M.

This is 8a, add 3b, subtract 4a.

This simplifies to 4a, add 3m.

CM is negative 4a, as it is the opposite direction, to the positive, which is D to C.

Here are some questions for you to try.

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

Here with the answers.

The vector DM is written as 2a, the line MC is also 2a.

The length MB is MC add CB.

So this is 2a add 2b.

The length AM is AD add DM.

So this is written as 2a subtract 2b.

ABCD is a trapezium, Point M is the midpoint of AD.

We're going to write the vector AD in terms of a and b.

This is 4a add a add b subtract 6a, which simplifies to b subtract a.

Next we're going to write the vector AM.

This is a 1/2 of AD, we can write it as a 1/2 multiplied by b subtract a.

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.

The vector DA, can be written as negative 3a, add 3b, add 5a, which is simplifies to 2a add 3b.

The length DM is 1/2 of DA.

This is written as a add 3/2b, the length AM is a 1/2 of the length AD.

AD is negative 2a subtract 3b, which means that AM is negative a subtract 3/2b.

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.

The length DN is written as 4a cause its a 1/2 of the length DC.

We know that DC is 2 lots of AB, So DC is 8a meaning that DM is 4a.

The length DN is a 1/2 of DB.

DB is 5a add b, which means that DN is 5/2a add a 1/2b.

MN is MD add DN.

This simplifies to a 1/2b subtract 3/2a.

Finally, AM is AD add DM, which simplifies to 3a subtract b.

That's all for this lesson.

Thanks for watching.