Lesson video

Hi, I'm Miss Davis.

In this lesson, we're going to be proving that two lines are perpendicular.

To identify if two lines up are perpendicular, we need to start by identifying the gradients of the lines and finding the product of these two gradients.

With this example, we can see that the gradient of line one is three, and the gradient of line two is -1/3.

To find the product of these two gradients, we're going to multiply them together.

Three multiplied by -1/3 gives a result of -1.

If two lines are perpendicular, then their gradients give a product of -1.

These two lines are perpendicular to one another as their gradient multiply to give -1.

In our next example, we've been given three pairs of equations of lines.

In the fist example, Line1 has a gradient of four, and Line2 has a gradient of -1/4.

Four multiplied by -1/4, gives a result of -1.

So these two lines are perpendicular.

In the second example, Line1 has a gradient of -2, and Line2 has a gradient of -1/2.

2 multiplied by -1/2 gives a result of one.

Therefore these two lines are not perpendicular.

With the third example, we need to write these equations so that y is the subject.

Line1 would be written as y= -3/2x + 2.

Line2 would be written as y= -5/3 + 2/3x.

The gradient of Line1 is -3/2.

And the gradient of Line2 is 2/3.

These two gradients multiplied together, give a result of -1.

Therefore these two lines are perpendicular.

Here's some questions for you to try.

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

Here are the answers, the gradients of the lines in parts a, c and d multiply to give -1.

Whereas impart b, the gradients multiply to give +1.

Therefore these two lines are not perpendicular.

That's all for this lesson.

Thanks for watching.