E1.3 Plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another.
Activity 1: Locate, Read and Describe the Translation of Points in the Four Quadrants of the Cartesian Plane
Here is a small corner of the city of Timmins represented on a Cartesian plane.
Image a cartesian plane on which there are points representing a community centre, a restaurant, a secondary school, a parc, a grocery store, an elementary school, a municipal library, and a medical centre.
a) Indicate the coordinates of the points that will allow you to locate the following places.
|
Locations |
Coordinates |
|
Public Library |
|
|
High School |
|
|
Sports Centre |
|
|
Medical Centre |
|
|
Elementary School |
|
|
Community Centre |
|
|
Grocery Store |
|
|
Park |
|
|
Restaurant |
b) As a result of discussions at City Council, the city of Timmins has decided to change the locations of some services. The plan below shows the new locations of these services in the column labelled Image (x, y). Use the information in the table to add the new locations on the Cartesian plane. Describe the movement of each.
| Coordinates | ||
|---|---|---|
| Locations | Initial point (x,y) | Image (x,y) |
|
Sports Centre |
(0, 0) |
(5, -2) |
|
Community Centre |
(2, 6) |
(-5, 7) |
|
Restaurant |
(3, 2) |
(3, 3) |
Source: translated from En avant les maths!, 6e année, ML, Sens de l’espace, p. 4-5.
Activity 2: Translations
Locate the points (4, 1), (-1, 3), (5, -7) and (-2, -6) on the Cartesian plane.
Perform the translation (x +1, y -3) at all coordinates. What do you notice? How could you describe the various translations?