Understanding Perpendicular Lines and Their Gradients

The video tutorial explains the concept of perpendicular lines, focusing on their gradients. It demonstrates that the gradients of perpendicular lines are negative reciprocals of each other. The tutorial provides examples and solves exam questions to illustrate how to find the gradient of a line perpendicular to a given line. It also covers how to write the equation of a line that is perpendicular to another line and passes through a specific point. The video concludes with identifying pairs of perpendicular lines from a set of options.

What is the gradient of a line that is perpendicular to a line with a gradient of 2?

• -2

• 2

• 1/2

• -1/2

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

• -1/3

• 1/3

• 3

• -3

How do you find the gradient of a line perpendicular to a given line?

• Subtract 1

• Take the reciprocal and change the sign

• Multiply by 2

• Add 1

A line has a gradient of -3. What is the gradient of a line perpendicular to it?

• -3

• 1/3

• -1/3

• 3

What is the equation of a line perpendicular to y = -2x + 1 that passes through the point (0, 3)?

• y = -1/2x + 3

• y = 2x + 3

• y = -2x + 3

• y = 1/2x + 3

Which of the following pairs of gradients represent perpendicular lines?

• 1/3 and 3

• 3 and -3

• 2 and -1/2

• -2 and 1/2

If a line has a gradient of 4/3, what is the gradient of a line perpendicular to it?

• 4/3

• -3/4

• 3/4

• -4/3

What is the gradient of a line perpendicular to y = 4x - 5?

• -4

• 1/4

• -1/4

• 4

A line passes through the point (2, 6) and is perpendicular to y = -2x + 1. What is its equation?

• y = 2x + 5

• y = -2x + 5

• y = -1/2x + 5

• y = 1/2x + 5

Which of the following gradients would make a line perpendicular to a line with a gradient of -5/2?

• 5/2

• -5/2

• -2/5

• 2/5