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Understanding Vectors in 2D: Coordinate Geometry and Distance Between Points

This lesson delves into the fundamentals of vectors in 2D coordinate geometry, focusing on vectors defined by two points, A(xA, yA) and B(xB, yB). It explores how to calculate the vector AB as the difference in coordinates, specifically AB = (xB - xA, yB - yA), and discusses the concept of vector direction and equality. Additionally, the lesson covers distance between two points using the length of the vector, denoted as |AB|. The principles presented serve as a foundation for more advanced topics in geometry.

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Understanding Vectors in 2D: Coordinate Geometry and Distance Between Points

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  1. Chapter 15: Vectors in 2D Lesson E: Vectors in Coordinate Geometry

  2. Vectors between two points Consider points A (xA, yA) In going from A to B xB-xA is the x-step yB-yA is the y-step Y B yB yB-yA A yA xB - xA X xA xB

  3. Vector between two points • Consequently, • AB = xB – xA yB – yA • if that is AB then BA is?

  4. Vector between two points • Notice • If O is (0,0) and A is (xA, yA) then • OA is xA yA y A(xA, yA) yA O x xA

  5. Distance between two Points • Distance between two points A and B is the length of AB (or BA) and is denoted IABI. • See example #1

  6. Vector Equality • Two vectors are equal if they have the same length and direction • Thus their x-steps are equal i.e., p=r and their y-steps are equal i.e., q=s p r q s = q s p r “If and only if” p=r and q=s

  7. See example

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