### The Transformation Simulation above is summarized in the notes below.

 Transformation Example original = ΔABC image = ΔA'B'C' Mapping Notation original = ΔABC image = ΔA'B'C' Translation (Slide) The object and image have the same orientation. Corresponding sides of the object and image are parallel -->>--. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (x+3, y+2) ordered pair: [3, 2] means 3 right and 2 up ---------------------------------- Additional Mapping Example (x, y) --> (x-4, y-5) ordered pair: [-4, -5] means left 4 down 5 as shown by the slide arrow: (x, y) --> (x+3, y+2)   ΔABC is moved 3 units right and 2 units up as shown by the slide arrow to the left. ΔABC is located at: A(7,4), B(5,2), C(3, 4) Image ΔA'B'C' is A'(7+3,4+2) B'(5+3,2+2) C'(3+3,4+2) or A'(10,6), B'(8,4), C'(6, 6) Reflection through the x-axis (Flip) The object and image are equidistant from a line of reflection. Segments joining corresponding sides of an object and image are   perpendicular to the reflection line. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (x, -y) (x, y) --> (x, -y) ΔABC is being flipped across the x-axis (y = 0). ΔABC is located at: A(4,6), B(4,2), C(2,2)Image ΔA'B'C' is A'(4,-6), B'(4,-2), C'(2,-2) Reflection through the y-axis (Flip) The object and image are equidistant from a line of reflection. Segments joining corresponding sides of an object and image are   perpendicular to the reflection line. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (-x, y) (x, y) --> (-x, y) ΔABC is being flipped across the y-axis (x = 0). ΔABC is located at: A(4,6), B(4,2), C(2,2) Image ΔA'B'C' is A'(-4,6), B'(-4,2), C'(-2,2) Reflection through y = x (Flip) The object and image are equidistant from a line of reflection. Segments joining corresponding sides of an object and image are   perpendicular to the reflection line. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (y, x) (x, y) --> (y, x) ΔABC is being flipped across the line y = x. ΔABC is located at: A(4,6), B(4,2), C(2,2) Image ΔA'B'C' is A'(6, 4), B'(2, 4), C'(2, 2) Reflection through y = - x (Flip) The object and image are equidistant from a line of reflection. Segments joining corresponding sides of an object and image are   perpendicular to the reflection line. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (-y, -x) (x, y) --> (-y, -x) ΔABC is being flipped across the line y = -x. ΔABC is located at: A(4,6), B(4,2), C(2,2) Image ΔA'B'C' is: A'(-6,-4), B'(-2,-4), C'(-2,-2) Reflection through x = 1 (Flip) The object and image are equidistant from a line of reflection. Segments joining corresponding sides of an object and image are   perpendicular to the reflection line. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (2-x, y) (x, y) --> (2-x, y) ΔABC is being flipped across the line x = 1. ΔABC is located at: A(4,6), B(4,2), C(2,2) Image ΔA'B'C' is: A'(-2,6), B'(-2,2), C'(0,2) Rotation about the origin half turn clockwise (cw) or half turn counterclockwise (ccw) The object and image are equidistant from a given point. The object and image are congruent (corresponding angles and sides are congruent). mapping (x, y) --> (-x, -y) turn center = origin (x, y) --> (-x, -y) ΔABC is rotated 1/2 turn around the origin (clockwise or counterclockwse. ΔABC is located at: A(-3,-4), B(-2,-1), C(-5,-5) Image ΔA'B'C' is: A'(3, 4), B'(2, 1), C'(5, 5) Rotation about the origin quarter turn clockwise (cw) or three quarter turn counterclockwise (ccw) The object and image are equidistant from a given point (turn centre). The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (y, -x) turn center = origin (x, y) --> (y, -x) ΔABC is rotated 1/4 turn around the origin. ΔABC is located at: A(-3,-4), B(-2,-1), C(-5,-5) Image ΔA'B'C' is: A'(-4, 3), B'(-1, 2), C'(-5, 5) Rotation about the originquarter turn counterclockwise (ccw) or three quarter turn clockwise (cw) The object and image are equidistant from a given point. The object and image are congruent (corresponding angles and sides are congruent). mapping: (x, y) --> (-y, x) turn center = origin (x, y) --> (-y, x) A(-3,-4), B(-2,-1), C(-5,-5) ΔABC is rotated 1/4 turn around the origin. Image ΔA'B'C' is: A'(4, -3), B'(1, -2), C'(5, -5) Dilatation about the origin (Enlargement or Reduction) The object and image are similar when the dilatation factor ¹ 1. (corresponding angles are congruent). The object and image are congruent when the dilatation factor = 1. (corresponding angles and sides are congruent). mapping: (x, y) --> (3x, 3y) dilatation centre = origin (x, y) --> (3x, 3y) ΔABC is being enlarged around the origin. A(2,3), B(2,1), C(1,1) Image ΔA'B'C' is: A'(6, 9), B'(6, 3), C'(3, 3)