Perform Congruence Transformations

Transformations: when you move or change a geometric figure in some way to produce a new figure. Image is what the new figure is called. Translation: is when we move every point on the figure, the same distance and direction. Reflection: is when we use a line of reflection to create a mirror image of the original figure. Rotation: Turns a figure about a fixed point called the center of rotation Congruence Transformations: changing the position of a figure without changing its size or shape. There are 3 types of transformations.

Coordinate Notation for a translation: (x,y) (x+a, y+b) Which shows that each point (x,y) of the blue figure is translated horizontally a units and vertically b units a b x y

Multiply the y coordinate by -1 (x,y) (x,-y) Multiply the x coordinate by -1 (x,y) (-x,y)  Reflection in the x-axis  Reflection in the y-axis y x y x (x,y) (x,-y) (-x,y) (x,y)

 90 clockwise Rotation  60 counterclockwise rotation y y xx

 Figure ABCD has the vertices A(-4, 3), B(-2, 4), C(-1, 1), and D(-3, 1). Sketch ABCD and its image after the translation (x, y)  (x+5, y-2).

 Figure WXYZ has the vertices W(-1, 2), X(2, 3), Y(5, 0), and Z(1, -1). Sketch WXYZ and its image after the translation (x, y)  (x-1, y+3).

 Use coordinate notation to describe the translation.  5 units right, 3 units up  7 units left, 4 units down