**Transformations** Translations, Reflections, Rotations & Dilations Notes for Foldable

**Translations** Common name:Slide(horizontally or vertically or both) Rule:Add each point in the figure to a given point Example:Translate ∆ABC by (3,-2). Original Points: A (-6,1) B (-1, -1) C (-3, 3) (Graph this on your grid ) +(3,-2)+(3,-2)+ (3,-2) New points A’ (-3, -1) B’ (2, -3) C’ (0, 1)

**Reflections** Common name:Flip (over the x-axis or y-axis) Rules: To reflect a point over the x-axis, keep the original x-coordinate and multiply the y-coordinate by -1. Example: A (4, -3) A’ (4, 3) To reflect a point over the y-axis, keep the original y-coordinate and multiply the x-coordinate by -1. Example: A (4, -3) A’ (-4, -3)

**Reflection Example** Choose one to graph in your foldable: Graph ∆PQR with vertices of: P(2, 1) Q(7, 3) R(3, 5) Example 1: Reflect ∆PQR over the x-axis P’(2, -1) Q’(7, -3) R’(3, -5) Example 2:Reflect ∆PQR over the y-axis P’(-2, 1) Q’(-7, 3) R’(-3, 5)

**Rotations** Common name:Turn Rules for rotating about the origin: (x, y) (-x, -y) 180˚ clockwise or counter-clockwise (x,y) (y, -x) 90˚ clockwise 270˚ counter-clockwise (x, y) (-y, x) 90˚ counter-clockwise 270˚ clockwise

**Rotation Examples** Graph ∆USA with vertices at U (3, 2) S(6, 3) and A(4, 6) Now rotate it 90˚counter-clockwise about the origin. U’ (-2, 3) S’ (-3, 6) A’ (-6, 4) Now rotate the original 180˚ about the origin. U” (-3, -2) S” (-6, -3) A” (-4, -6) Lastly, rotate the original 270˚ counter-clockwise about the origin. U”’ (2, -3) S”’ (3, -6) A”’ (6, -4)

**Dilations ** Common name: Enlarge or Shrink Dilate means “to make wide or larger.” Dilations change the size, but not the shape of a figure. A figure can be enlarged or reduced through dilation. Rule:When using the origin as the center of dilation, we multiply each point in an ordered pair by the scale factor. ***Scale factor greater than 1 = an enlarged figure ***Scale factor less than 1 = a smaller image

**Dilation Example** Example: Graph rectangle MATH with vertices at: M (-3, 2) A (3, 2) T (-3, -2) H (3, -2) Now dilate MATH by a scale factor of 2 with the origin as the center of dilation. What are the vertices of the new image? Graph on your paper. M’ (-6. 4) A’ (6, 4) T’ (-6, -4) H’ (6, -4)