Midpoint, Length And Perpendicular Bisector
Overview
Give the coordinates of two points and you can answer three natural questions at once: where is the point exactly between them, how far apart are they, and what line cuts the join in half at a right angle? These are the midpoint, the length, and the perpendicular bisector, three pillars of coordinate geometry.
In this lesson you will learn the midpoint and distance formulas and combine them with the perpendicular-gradient rule to construct a perpendicular bisector. The bisector pulls everything together: it passes through the midpoint and has the negative-reciprocal gradient of the segment it cuts.
Objectives
- Solve problems involving the midpoint and length of a line, including finding and using the equation of a perpendicular bisector.
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Lesson Evaluation
Congratulations on completing the lesson on Midpoint, Length And Perpendicular Bisector. 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 the midpoint of A(2, 3) and B(8, 7)? A. (5, 5) B. (6, 4) C. (10, 10) D. (3, 2) Answer: A
- What is the length AB for A(2, 3) and B(8, 7)? A. sqrt(20) B. sqrt(52) C. 10 D. sqrt(100) Answer: B
- The gradient of AB for A(2, 3) and B(8, 7) is: A. 2/3 B. 3/2 C. -2/3 D. 4 Answer: A
- The gradient of the perpendicular bisector of AB (A(2,3), B(8,7)) is: A. 2/3 B. -2/3 C. 3/2 D. -3/2 Answer: D
- Which formula uses a difference and a square? A. Midpoint B. Length (distance) C. Gradient sum D. Average Answer: B
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