Transformations & Similarity

What you’ll learn

• Reflecting across $x=a$ sends $x$ to $2a-x$; identify a move from two points, apply sequences in order, and remember that rigid motions keep lengths while dilations scale them.
• Translations add $(h,k)$ to coordinates; reflections flip signs according to the mirror line; $90°$ CCW rotation about the origin sends $(x,y)$ to $(-y,x)$.
• Congruent figures match size and shape via rigid motions; similar figures have equal angles and side lengths in proportion.
• Scale factor $k$ multiplies lengths; a dilation $(x,y) \mapsto (kx,ky)$ about the origin preserves angle measures.
• Order matters when you chain moves: reflect then translate may land differently than translate then reflect.
• Coordinate rules connect to distance and slope tools when you verify side lengths after a move.