Translations, Reflections, and Rotations

A transformation is a change in a figure's position. Translations, rotations, and reflections are types of transformations

A translation is the movement of a figure from one position to another without turning it

A rotation is a transformation involving the turning or spinning of a figure around a fixed point called the centre of rotation

The mirror image produced by flipping a figure over a line is called a reflection. The line is called the line of reflection

A translation is the movement of a figure from one position to another without turning it

The translation can be described using an ordered pair. A translation up or to the right is positive. A translation down or to the left is negative. For example: (5, -2) means a translation 5 units right and 2 units down

To translate a polygon by (m, n), move each vertex of the polygon m units left/right and n units up/down. Connect the new vertices to form the image

The new vertices can also be found by adding m to the x-coordinate and n to the y-coordinate

A rotation is a transformation involving the turning or spinning of a figure around a fixed point called the centre of rotation

To rotate a Δ ABC 90° counterclockwise about O, draw OA' so that m∠A'OA = 90° and OA' = OA. Repeat the step for B and C. Connect the points to form the image

The mirror image produced by flipping a figure over a line is called a reflection. The line is called the line of reflection

The y-coordinate of a point reflected across the x-axis is the opposite of the y-coordinate of the original point. The x coordinate remains the same

The x-coordinate of a point reflected across the y-axis is the opposite of the x-coordinate of the original point. The y coordinate remains the same

When a figure is reflected over the origin, both the x and y coordinates are the negative of the original coordinates

A dilation is a transformation that changes the size, but not the shape, of a figure

After a dilation, the image of a figure is similar to the original figure

A dilation enlarges or reduces a figure. The scale factor tells how much the figure is enlarged or reduced

To plot an enlarged / reduced figure, multiply the coordinates of each vertex of the figure by the scale factor. Plot and join the new coordinates