12.6 Matrices & Transformations. Graphical transformations (reflections & rotations) can be interpreted using matrices. (point) general or specific 

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Presentation transcript:

12.6 Matrices & Transformations

Graphical transformations (reflections & rotations) can be interpreted using matrices. (point) general or specific  new point Def: A 2-by-2 transformation matrix is of the form and it maps each point P(x, y) to its image point P' (x', y') Reflection wrt the x-axis Reflection wrt the y-axis

Ex 1) 2 Truths and a Lie Each of the following illustrates the transformation of a point. Find and fix the error. a) b) c) should be

find There are also matrices that represent rotations. If you are asked to rotate  ° We can apply a rotation transformation matrix as well as find out what rotation a combo of transformations is the same as. We can also use the transformation matrix with an equation. Ex 2) Find and graph the image of f (x) = x 2 – x + 2 under T y-axis.

Ex 3) Find the image. Ex 4) Find the transformation formed by the indicated product. cosθ sinθ Where does cosθ = 0 and sinθ = 1? at 90° so, equivalent to R 90° *you will do this in your homework

Homework #1206 Pg 637 #3–15 odd, 19–23 all, 27, 31, 33, 38, 39