Perpendicular Lines and Gradients

This video tutorial explains the concept of perpendicular lines, which intersect at a 90-degree angle. It demonstrates how to verify perpendicularity by multiplying gradients, using the formula m1 * m2 = -1. The video includes example problems to practice this concept and explains how to find the gradient of a perpendicular line. It concludes with a brief mention of finding the equation of a perpendicular line, which is covered in another video.

What is the defining characteristic of perpendicular lines?

• They intersect at a 90-degree angle.

• They never intersect.

• They are parallel.

• They have the same slope.

Which of the following equations represents a line perpendicular to y = 2x - 2?

• y = -1/2x + 8

• y = 1/2x - 4

• y = -2x + 5

• y = 2x + 3

How can you verify if two lines are perpendicular using their gradients?

• Their gradients add up to zero.

• Their gradients are equal.

• The product of their gradients is -1.

• The product of their gradients is 1.

If a line has a gradient of 2, what should be the gradient of a line perpendicular to it?

• -1/2

• 1/2

• 2

• -2

In the example problem, what are the gradients of the lines given in the first question?

• 1/3 and -3

• 1/2 and 3

• 2 and -1/2

• 3/2 and -2/3

What is the result of multiplying the gradients 1/2 and 3?

• 1

• 3/2

• -1

• 2

In the second example problem, what is the first step to find the gradient of the line y = 3x + 8?

• Multiply by 2

• Divide by 2

• Subtract 2

• Add 2

After converting y = 3x + 8 to slope-intercept form, what is the gradient?

• -2/3

• 3/2

• 1/3

• 3

What is the product of the gradients 3/2 and -2/3?

• 0

• 2

• 1

• -1

If a line has a gradient of 1/3, what is the gradient of a line perpendicular to it?

• 3

• -3

• -1/3

• 1/3