Math - Transformations
Dilation (Englare, Reduce), Effect, Precervence, Image and pre-image, Scale Factor, Equation
- Look at the pre-image and dilate from there, image has a mark, prime (') - If larger than 1 it is enlarged - If if the scale factor is 1 it stays the same (1x,1y) or (x,y) - if smaller than 1 it is reduced - To find scale factor, ratio - new/original or image/pre-image - The orientation of the figure and vertices are the not changed - The congruence is changed
Reflection (Flip), Effect, Precervence, Image and pre-image, Equations
- Look at the pre-image and reflect from there, image has a mark, prime (') - If reflected over y-axis (-x,y), x values became their opposites (2,6 / -2,6) - If reflected over x- axis (x, -y), y values became their opposites (2, -7 / 2,7) - Orientation of figure and vertices changed - The image and pre-image are congruent
Translations (Slides), Effect, Precervence, Image and pre-image, Equation
- Look at the pre-image and translate from there, image has a mark, prime (') - Increased 9 right, Decreased 2 down (x-9,y-2) - Translation Preserve congruence and orientation of figure and the vertices
Rotations (Turn), Effect, Precervence, Image and pre-image, Equation
- Orientation of figure sometimes change - Orientation of vertices are preserved - Congruence is Always preserved - Look at the pre-image and rotate from there, image has a mark, prime (') - 90 clockwise/270 counterclockwise (x,y) - (y, -x) - 180 clockwise/180 counterclockwise (x,y) - (-x, -y) - 270 clockwise - 90 counterclockwise (x,y) - (-y, x) - Sign than switch
Congruence
Congruence refers to weather the pre-image and image have the same size and shape.
Congruency
If a transformation produces an image with the same shape and size was the pre-image, the figure are congruent. The figure of congruence is ≅. ABC ≅A'B'C'
Similarity
If transformation produces an image with proportional sides and congruent angles, the figures are similar. the symbol for similarity id ∼, ABC ∼ A'B'C'
Orientation of the figure
Orientation of the figure refer to weather the pre-image and image are facing the same direction on the coordinate plane.
Orientation of the vertices
Orientation of the vertices referred to the order in which the vertices are labeled, clockwise, counterclockwise.
