Student Exploration: Adding Vectors Vocabulary: component, initial point, magnitude, resultant, scalar, terminal point, vector Prior Knowledge Questions (Do these BEFORE using the Gizmo.) Starting at her house (point A), Ava drives 5 miles east to visit her friend Bernice (point B). She then drives 12 miles north to visit Christine (point C). Finally, she drives directly back home. 12 miles 1. Sketch the straight path from point C to point A on the diagram to the right. How can you use the figure formed to find the length of the straight path from point C to point A? 5 miles 2. Calculate the distance from point C to point A. Show your work in the space to the right. Distance = Gizmo Warm-up A vector is a representation of something with both size, or magnitude, and direction. For example, a moving car can be represented by a vector because the car has both speed (magnitude) and direction. On a graph, vectors are represented by arrows. The base of the arrow is the initial point and the tip of the arrow is the terminal point 1. Drag the initial point (the circle) of vector a to the origin. This vector is now said to be in standard position. Notice the components of a shown in brackets like this: <_ _>. What are the components of a? 2. Drag the initial point of vector a around. A. Does this change the components of a? B. Compare the coordinates of the initial and terminal points of a to its components