Apply coordinate rules for translations and reflections to find image points, and explain why these transformations preserve distance and angle measure.
A transformation moves every point of a figure according to some rule, turning a preimage into an image. The transformations that matter most this year are rigid motions (isometries): translations, reflections, and rotations, each of which preserves both distance and angle measure -- the image is always an exact, same-size copy of the preimage, just relocated. We label an image point with the same letter as its preimage plus the word "prime," so the image of point A is written A-prime, the image of B is B-prime, and so on.
A translation slides every point the same distance in the same direction -- on the coordinate plane, the rule (x, y) -> (x + a, y + b) shifts every point a units horizontally and b units vertically. A reflection flips every point over a line of reflection to its mirror image on the opposite side, the same distance from the line. Three coordinate rules cover the reflections used most: over the x-axis, (x, y) -> (x, -y); over the y-axis, (x, y) -> (-x, y); over the line y = x, (x, y) -> (y, x), swapping the coordinates.
Mastery looks like: They apply translation and reflection coordinate rules correctly to find image points and can explain why these transformations preserve distance and angle measure.
Common stumbles: Negating the wrong coordinate in a reflection; applying a translation to only some of the vertices instead of every point.
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