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4-6 Translations and Vectors

4-6 Translations and Vectors. We have seen translations as compositions of reflections. Today, we will be using what we know about magnitude and direction and translating in a slightly different way. What is a vector?. A vector is a quantity characterized by its magnitude and direction.

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4-6 Translations and Vectors

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  1. 4-6 Translations and Vectors We have seen translations as compositions of reflections. Today, we will be using what we know about magnitude and direction and translating in a slightly different way.

  2. What is a vector? • A vector is a quantity characterized by its magnitude and direction. • Magnitude = how much • Direction = which way • What does it look like?

  3. A v • A vector looks like a RAY when you draw it • Vector or • The length of the arrow shows how far to translate each point, and the direction shows where to translate. • What is the difference between a RAY and a VECTOR?? B

  4. Vectors in Synthetic Geometry (i.e. vectors on the drawing plane) • Given a figure and a vector, how do you translate it? • Identify the magnitude and direction of the vector • Translate each key point (vertex) of the figure by that amount in that direction • Connect the dots!

  5. Vectors in Coordinate-Plane Geometry (Remember, values on the coordinate plane have an x-component and a y-component) • Vector <a,b> • Ex. Triangle DEF has vertices D(-3, -1), E(0,4),and F(2,2). Translate this triangle by the vector <4, -2>. • What do you do to the x-values? What do you do to the y-values?

  6. Motion Rule Notation D(-3, -1) E(0,4) F(2, 2) Vector = <4 ,-2> D’ = (-3+4, -1-2) = (1, -3) E’ = (0+4, 4-2) = (4, 2) F’ = (2+4, 2-2) = (6, 0) Can we generalize this for a standard notation?

  7. Motion Rule Notation Given any point (x, y) and any vector <a, b> the translation can be described as… (x, y)  (x+a, y+b) preimagetranlated image translated image of the x-coordinate of the y-coordinate AND IF YOU DO THIS TO EVERY VERTEX OF A FIGURE, YOU CAN TRANLATE THE WHOLE THING!!

  8. Describe the vector shown below: What do you name it? < , > Q What would the motion rule notation look like? P What is the length (MAGNITUDE) of this vector?

  9. Describe the vector shown below: What do you name it? S < , > What would the motion rule notation look like? T What is the length (MAGNITUDE) of this vector?

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