Perpendicular Lines
Overview
Two lines are perpendicular when they meet at a right angle, and in coordinate geometry this gives a beautifully simple rule: their gradients multiply to give \(-1\). Knowing this lets you find the equation of a line at right angles to any given line.
In this lesson (Extended tier) you will find the gradient and equation of a straight line perpendicular to a given line, using the rule that perpendicular gradients multiply to \(-1\).
Objectives
- Find the gradient and equation of a straight line perpendicular to a given line.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Perpendicular Lines. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is true of the gradients of two perpendicular lines? A. They are equal B. They add to 0 C. They multiply to -1 D. One is always 0 Answer: C
- A line has gradient 2. The gradient of a perpendicular line is: A. 2 B. -2 C. 1/2 D. -1/2 Answer: D
- A line has gradient -3. The gradient of a perpendicular line is: A. 3 B. 1/3 C. -1/3 D. -3 Answer: B
- The line perpendicular to y = 2x + 1 through (0, 3) is: A. y = 2x + 3 B. y = -1/2 x + 3 C. y = -2x + 3 D. y = 1/2 x + 3 Answer: B
- The perpendicular gradient is found by taking the: A. same value B. negative C. reciprocal D. negative reciprocal Answer: D
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