Algebra I Lesson 10
Number Relations

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Introduction to Linear Relations

Instruction 10-1

Ordered Pairs |Relations | Equations as Relations | Graphing Linear Relations | Summary
ORDERED PAIRS  
CA GR7 MG 3.2, CA Algebra 17.0
There are an infinite number of points in the coordinate plane below. These points are all different from each other (Figure 10.1). The coordinate plane depicted below should have arrows at the end of each line.


Figure 10.1

How we can distinguish these points? It is very simple. The distances of each point from x and y axes make them different. We use the distances of any point from x and y axes to identify the point.

The distance of a point from x-axis is called y-coordinate and its distance from y-axis is called x-coordinate. These coordinates are denoted as an ordered pair in the form of (a, b), where a represents the x-coordinate and b represents the y-coordinate of a point. In Figure 10.2, some points are shown using their coordinates. Again the lines need arrows on both ends. The coordinates are not shown on the coordinate axis below – they need to be. The points also need to be labeled with their coordinates, not with just their letters.


 

Figure 10.2

To find the location of any point, simply follow the steps below:

(a) Find a point on x-axis whose x-coordinate is equal to the x-coordinate of the given point (Point A in Figure 10.3).

(b) Draw a perpendicular segment from Point A upward or downward. If y-coordinate of the point is a positive number, draw it upward. If it is a negative number, draw the segment downward ( in Figure 10.3)

(c) Find a point B on y-axis whose coordinate is the same as the y- coordinate of the given number (Point B in Figure 10.3).

(d) Draw a perpendicular segment to y-axis at this point. Choose its direction in a quadrant where the previous segment is located ( in Figure 10.3).

(e) M, the point of intersection of and is the given point.

An alternate way to think of plotting a point on a coordinate axis is:

  1. Think of a building with a bank of elevators.
     

  2. The first number is the number of the ‘elevator’ you want to get on. If it is positive, it is to the right of the vertical line (otherwise known as the y-axis). If it is negative, it is to the left of the vertical line.
     

  3. The second number tells you what ‘floor’ you want to get out on. If it is a positive number, you will go up. If it is a negative number, you will go down.

 

 

Figure 10.3

Practice 1

Locate points M(–3, 4), N(3, 3), P(4, 0), and Q(–2, –3) in a coordinate plane.

Solution

Figure 10.4

The quadrants of a coordinate axis are labelled counterclockwise beginning with the upper right hand quadrant labeled I. The upper left hand quadrant is II, the lower left hand quadrant is III and the lower right hand quadrant is IV. Notice the signs on the coordinates that are located in each quadrant.
 

Practice 2

Determine the quadrant in which each point is located.

 

A(–3, 7), B(5, 5), C(4, –5), D(–4, –5), E(–11, 11), F(11, –11), and G(4, 4)

 

Answer

 

Point

A

B

C

D

E

F

G

Quadrant

II

I

IV

III

II

IV

I

 

Practical Exercise 1

Locate the points A(–3, 2), B(3, 4), C(2, –4), and D(–1, –3). Connect the points in the same order.

 

Answer

Links for Students, Parents and Teachers

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