Lesson video

Hi.

I'm Miss Davies.

In this lesson, we're going to be working out the equation of the perpendicular bisector of a line segment.

To bisect a line or an angle is to cut it into two equal pieces.

By knowing the midpoint of the line segment, we will give the coordinate for the perpendicular line to go through.

Looking at this example, we've been asked to find the equation of the perpendicular bisector to the line segment M.

The midpoint of M is negative 1.

5, negative two.

Next, we're going to work out the gradient, which is two.

This means that the perpendicular bisector has a gradient of negative 1/2.

Using y equals mx add c, we can find that the equation for this line is y is equal to negative 1/2x add c.

We can then substitute in the coordinates of the midpoint to give negative two is equal to negative 1/2 multiplied by negative 1.

5 add c.

Negative 1/2 multiplied by negative 1.

5 is positive 0.

75.

This means that the value of c is negative 2.

75.

The equation of the perpendicular bisector is therefore y is equal to negative 1/2x subtract 2.

75.

Here is a question for you to try.

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

Here is the answer.

The gradient of line segment M is negative 2/5, meaning the gradient of the perpendicular bisector is five over two, or 2.

5.

The midpoint of the line segment M is negative 3.

5, two.

This gives a final equation of y equals five over two x add 10 3/4, or you could have written it as y equals 2.

5x add 10.

75.

In the next example, we're finding the equation of the perpendicular bisector between two coordinates.

Let's start by roughly plotting these two coordinates on a set of axes.

From this, we can see that the x difference is 10 and the y difference is 18.

This means that the gradient of this line is negative 18 over 10, which simplifies to negative nine over five.

We can also see that the midpoint is two, negative one.

Now that we found the gradient of the line, we can say that the gradient of the perpendicular is five over nine.

We can substitute this into y equals mx add c to give y is equal to 5/9x add c.

Using the coordinates of the midpoint, we can state that negative one is equal to five over nine multiplied by two add c.

Five over nine multiplied by two is 10 over nine.

We subtract this from both sides.

It gives us that c is equal to negative 19 over nine.

This means that the equation of the perpendicular bisector is y is equal to negative 5/9x subtract 19 over nine.

Here is a question for you to try.

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

Here is the answer.

The gradient of the connecting line is three, meaning the gradient of the perpendicular bisector is negative 1/3.

The midpoint of the connecting line between the two coordinates is negative two, four.

That's all for this lesson.

Thanks for watching.