Chapter Notes: Location and Movement, Translations

Translations

• A translation is a movement of a shape in a straight line without changing its size, shape, or orientation.
• Translations are described by specifying the distance moved left or right (horizontal) and up or down (vertical).
• Example: Moving a shape 2 squares right and 1 square down translates each vertex by the same distance and direction.
• Example: Translating shape A to shape B by 4 squares left and 1 square down moves each vertex of shape A by (4 left, 1 down).

Properties of translations:

• Each vertex of the original shape moves the same distance and direction to form the translated shape.
• Lines connecting corresponding vertices of the original and translated shapes are parallel and of equal length.
• A shape that is rotated, resized, or flipped is not a translation, as these actions change the shape's orientation or size.

Shapes on a Coordinate Grid

• Coordinates on a grid are written as (x, y), where x is the horizontal position and y is the vertical position.
• Shapes can be plotted or translated on a coordinate grid using their vertices' coordinates.

Finding vertices of shapes:

• Example: For a rectangle with vertices at (1, 3), (5, 3), (5, 4), the fourth vertex is (1, 4), forming a closed rectangle.
• Example: For a rectangle with vertices at (6, 3), (6, 7), (8, 3), the fourth vertex is (8, 7).

Translations on a coordinate grid:

• Example: Translating shape A by 5 right and 2 up to shape B changes each vertex's coordinates by adding (+5, +2).
• Reverse translation (B to A) subtracts the same values: (-5, -2).

Patterns in coordinates:

• Example: Coordinates (0, 2), (1, 4), (2, 6), (3, 8) form a linear pattern where y = 2x + 2, continuing with (4, 10), (5, 12).