Unit A: Geometry

Chapter 2: Transformations

Using Grids to Demonstrate Translations

Describing a translation requires a method to describe movement horizontally and vertically. Often this is done using a grid, such as you might find on a map or graph. Recall that when stating coordinates on a graph, the horizontal location is given first followed by the vertical location. The coordinates for the centre of star A in the diagram are (4, –2). The coordinates for the centre of image A' are (–3, 3). The symbol A' is pronounced “A prime.” In geometry, the term prime is used to identify the image of a transformed object.

Star A is translated horizontally 7 units to the left and vertically 5 units up to form image A'. In a translation, the size and shape of the object does not change, only the position changes.

Example 1

Chevy has a map. He locates himself at F4. He is trying to get to the convenience store at D7. How far horizontally and vertically must he walk to get there if each square

Solution

The convenience store is located at D7. Chevy must travel two squares, or 100 m west (horizontal distance on the map), and three squares, or 150 m north (vertical distance on the map), to get to the convenience store.