Transformations and Dilations Algebraic Rules

Transformations and Dilations Algebraic Rules

• Reflection across the y-axis alters coordinates from (x,y) to (-x,y), changing the sign of the x-coordinate.
• Reflection across the x-axis changes coordinates from (x,y) to (x,-y), altering the sign of the y-coordinate.
• Dilation with a scale factor of three transforms coordinates to (3x,3y), enlarging the figure by three times.
• A dilation with a scale factor of one-half alters coordinates to (1/2x, 1/2y), reducing the figure to half its size.
• A rotation of 90° clockwise changes coordinates from (x,y) to (y,-x), shifting positions in a circular manner.
• A rotation of 90° counterclockwise alters coordinates from (x,y) to (-y,x), also rotating points circularly but in the opposite direction.
• The translation rule (x,y)→(x + 5, y - 3) moves points 5 units to the right and 3 units down on a Cartesian plane.
• The dilation rule (x,y)→(2x, 2y) expands figures by a scale factor of 2, doubling the size of the original figure.
• The transformation (x,y)→(-x,y) indicates reflection across the y-axis, which flips the figure horizontally.
• The transformation (x,y)→(-x,-y) represents a 180° rotation, flipping the figure across both axes.
• Translating points left 4 and up 7 is described by (x, y)→(x-4, y + 7), moving the position of points effectively in two directions.
• A dilation represented by (x,y)→(4x, 4y) increases the size of the figure by a scale factor of 4, quadrupling its dimensions.