105
The coordinate grid
Textbook: Part 3, lesson 105, pp. 112–114
GoalThe coordinate grid: axes OX and OY; the coordinates (x; y) of a point.
New words
coordinate grid · koordinata burchagiOX axis (horizontal) · OX o‘qiOY axis (vertical) · OY o‘qiorigin · sanoq boshi
Explanation
To state the position of a point on a plane exactly we draw two number rays: one horizontal (the OX axis) and one vertical (the OY axis). They meet at a right angle at 0, the origin; this figure is called a coordinate grid. A point is written with two numbers: first the number of steps along OX, then along OY. To reach A(7; 4) we go 7 steps right from 0 and then 4 steps up. The order matters: (7; 4) and (4; 7) are different points.
Worked examples
B(3; 5): 3 steps right and 5 steps up – altogether 3 + 5 = 8 steps.
(2; 0), (5; 0), (8; 0) all have second coordinate 0, so they lie on the OX axis. (0; 3) and (0; 5) lie on the OY axis.
Class activity
“Battleships”: on a grid each child hides a ship (3 points). A partner calls coordinates (“(4; 2)”) to find it. Remind that the first number is horizontal and the second is vertical.
Practice
1
How many steps in all are needed to reach A(7; 4) (first right, then up)?
11
2
In the point (3; 5), how many horizontal steps are there?
3
3
What is the area in square units of the rectangle with vertices A(2; 1), B(2; 4), C(7; 4), D(7; 1)? (AB = 3, BC = 5)
15
4
Which axis does the point (5; 0) lie on?
OX
5
On a map 1 mm is 200 m in reality. Two objects are 15 mm apart on the map. How many metres is the real distance?
3000