Transformations Vocab

• A reflection is a transformation using a line as a mirror
• Reflections can be over the x-axis, over the y-axis, over line y=x and over line y=-x
• A reflection over y=x is (a, b) to (b, a); a reflection over y=-x is (a, b) to (-b, -a)
• Write coordinates of pre-image and image before graphing
• For x-axis and y-axis reflections count the # of jumps left/right/down/up
• "Words" means to describe in words what happened in a reflection
• A rotation is a figure turned around the center of rotation; it is an isometry
• Lines drawn from the center of rotation to an image point and its pre-image point makes an angle of rotation
• A counterclockwise 90 degrees rotation is (a, b) to (-b, a)
• A counterclockwise 180 rotation is (a, b) to (-a, -b)
• A counterclockwise 270 rotation is (a, b) to (b, -a)
• In 180 degree rotation points connected should form a straight line
• Line symmetry is when a figure can be mapped onto itself by a reflection
• Rotational symmetry is when a figure can be rotated and its image is identical to the original
• Figures can have multiple lines of symmetry
• To find the degree of rotational symmetry in a regular polygon its 360/n
• A translation moves every point of a figure to a new point; can be moved left, right, up, or down; only its position changes not shape
• The mapping rule/coordinate notation is (x, y) --> (x+a, y+b)
• Words is a description of the translation a pre-image will undergo
• A vector is ⟨change in x, change in y⟩; has magnitude and direction
• A dilation stretches or shrinks a figure; creates similar figure
• Scale factor of a dilation: ratio of a side length of the image to the related side length of the pre-image
• Magnitude formula√(x2 + y2)
• To find the vector endpoint take the point and subtract/add by the vector
• A stretch expands or contracts a figure in 1 direction; either horizontally/vertically; result is not congruent or similar
• A glide reflection is a combination of transformations (2): a translation horizontally/vertically and a reflection by line k