Plotting Integers on the Coordinate Plane

The Coordinate Plane

A coordinate plane is formed by two perpendicular lines that intersect, or cross.  One line is vertical and the other is horizontal. 

Axes

The perpendicular lines that cross are called axes (plural).  Each line is called an axis (singular).

• The horizontal axis is called the x-axis.
  
• The vertical axis is called the y-axis.
  

Origin (0, 0)

The point where the two axes intersect is called the origin.  At this point both the x-coordinate and the y-coordinate are zero. It is named by the ordered pair (0, 0).

Positive and Negative Values

• x-coordinates to the right of zero are positive.
• x-coordinates to the left of zero are negative.

• y-coordinates rising up vertically from zero are positive.
• y-coordinates descending down vertically from zero are negative.

Ordered Pairs

Every point on a coordinate plane is named by an ordered pair, (x, y).  It is called an "ordered" pair because the order matters. 

The first number in the pair tells the x-coordinate, or the number of units to move along the horizontal axis. 

• If the number is positive, move to the right from the origin.
• If the number is negative, move to the left from the origin.
  

The second number in the ordered pair tells the y-coordinate, or the number of units to move along the vertical axis.

• If the number is positive, move up from the origin.
• If the number is negative, move down from the origin.

Quadrants

Quadrants are sections of the coordinate plane.  There are four quadrants, or sections. 

These are numbered with Roman Numerals I, II, III, and IV.  The numbering starts in the upper right corner and moves in a counter-clockwise direction.

Coordinate Values

Note how the x-coordinate and y-coordinate values change between positive and negative values in each quadrant.

Plot the points given on the coordinate plane below. 

Discuss their relationship to the y-axis.

• Point A: (5, 4)
  
• Point B: (-5, 4)

Practice

1.  Plot and label the following points:

Point A: (5, 2)

Point B:  (-3, 1)

Point C: (-4, -8)

Point D: (3, -7)

2.  Plot and label the following points. 

Point A: (3, 3)

Point B:  (-3, 3)

Point C: (-3, -3)

Point D: (3, -3)

What shape will be formed if you connect the dots in the order A, B, C, and D?

3.  Which quadrant of the coordinate plane contains negative values for both x and y?

4.  The point (-2, -3) is graphed on the coordinate plane below.

What will the new coordinates be if this point is reflected across the y-axis?

5.  The point (-2, -3) is graphed on the coordinate plane below.

What will the new coordinates be if this point is reflected across the x-axis?

Answers

1.

2.
square

3.  Quadrant III

4.  (2, -3)

5.  (-2, 3)