Lesson video

Hi, I Miss Davies.

In this lesson, we're going to be working out the equation of a line perpendicular to another that passes through a given point.

Line M and Line L1 are perpendicular.

Line 2 is also perpendicular to line M.

And so is line L3.

What is the same and what is different about these three lines? They all have the same gradient, but they have different Y and X intercepts.

We have been asked in this first example to find the equation of the line perpendicular to line M that passes through point A.

The first thing we are going to work out is the gradient of line M.

Line M has a gradient of 2.

This means that the line perpendicular has a gradient of -1/2 as the two gradients of perpendicular lines multiply to give -1.

Now that we have worked out the gradient of the perpendicular line, we can substitute that into Y equals Mx plus c.

We can then use the coordinate of point A to find the Y intercept.

Point A is the coordinate 6, 2.

This means that x is equal to 6 when Y is equal to 2.

This gives us the equation 2 is equal to -1/2 multiplied by 6 add C.

1/2 multiplied by 6 is -3.

This means that the value for C is 5.

This gives us the equation of the line Y equals -1/2x add 5.

In this next example, we are going to find the line perpendicular to line M that passes through point B.

The gradient of line M is -1/20.

The gradient of the perpendicular is therefore 20.

We can substitute this in to Y equals Mx add c to give us Y is equal to 20x add c.

Using the values at the coordinate B, which is -1, -7, we can say that -7 is equal to 20 multiplied by -1 add c.

This then gives us that -7 is equal to -20 add c.

This gives us the value for c of 13.

This means that the equation of the perpendicular is Y is equal to 20x add 13.

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 M is 1/3 as for every three units it moves to the right it moves one unit up.

This means that the gradient of the perpendicular line is -3.

In our next example, we've been asked to find the equation of the line that is perpendicular to Y equals 2x add 5 that passes through the point 10, -1.

The gradient of the line Y is equal to 2x add five is 2.

This means that the gradient of the perpendicular is -1/2.

We can substitute this in to give the equation Y is equal to -1/2x add c.

Using the X and Y values of the coordinate given, we can say that -1 is equal to -1/2 multiplied by 10 add c.

1/2 multiplied by 10 is -5.

This means that the value for c is 4.

The equation of the line perpendicular to line M is Y equals -1/2x add 4.

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 M is -5.

This means that the gradient of the perpendicular is 1/5 as the two gradients of perpendicular lines multiply to give -1.

That's all for this lesson.

Thanks for watching.