13.4 Vectors Objective: Sketch, find the length of, and name vectors.
Examples: • Boat Ride • Airplane
• **Vectors have BOTH magnitude and direction 02/28/13
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For the following three exercises (four slides): • Please use the points to find the necessary information for vector AB: A(4, 2) and B(-6, 3) Please sketch these points‌
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Information about Vectors: • They have a starting point and an ending point. • They MUST start at the first point and end at the second point. • Notation: 02/28/13
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To Find Direction AKA Naming the Vector: • (change in x, change in y) • (x2 – x1, y2 – y1) • Notation: • **Note: You MUST take x2 – x1. • Find the vector AB. 02/28/13
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To Sketch ANY vector: • Pick any point on the graph to start… • Then graph using the x and y coordinates! • Sketch vector AB in three different locations. 02/28/13
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To find length: • You know the drill… • DISTANCE FORMULA • Notation: • Find the length of vector AB.
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Example 1 - P(-5, 4) Q(1, 2) • Sketch the vector PQ. • Find the vector PQ. • Find the length of vector PQ.
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Ex. 2 - Scalar Multiplication • Sketch AND write the following vectors: • RS and –RS if RS = (1,2)
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Ex. 3 – Vector Addition • Vector PQ is the vector (4, 1) • Vector QR is the vector (2, 3) • Add these vectors…see board for details…
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Vectors…Again • Please complete the following problem in your notes for 13.4 • Given the following points, find, sketch, and find the length of vector GH. • G (-5, 3) and H (-3, 7) 02/28/13
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Ex 4. – Parallel Vectors • Arrows representing them have the same or opposite directions. • What else do we know about parallel lines? • Show that (9, -6) and (-6, 4) are parallel vectors… 02/28/13
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Ex. 5 – Perpendicular Vectors • Arrows representing them are perpendicular • How could you show that vectors are perpendicular? • Show that (9, -6) and (2, 3) are perpendicular vectors… 02/28/13
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13.5 Midpoint • Objective: Find the midpoint of a segment and find one point given the midpoint and the other point of a segment.
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Example 1 • Find the midpoint of the segment that joins: • D (3, 3) and E (9, 3)
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Midpoint Formula • See board for formula…
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Example 2 • Find the midpoint of the segment that joins the points (-11, 3) and (8, -7)
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Example 3 • M (4, -2) is the midpoint of segment AB. If A is (2, -5), find the coordinates of B.
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Class work… • Page 542 • 16-19
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Homework… • Page 545 • 1-10 • CLASS EX.
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• Page 541 • 1-8 • CLASS EX.
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