Math

Plot Points With Given Ordered Pairs

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Now you will plot points with given ordered pairs. When you read the ordered pair, (a,b), recall that the first coordinate, a, is the x-coordinate and the second coordinate, b, is the y-coordinate. We always start at the origin, (0,0), and move a units to the right or left (right if a is positive, left if negative) and then b units up or down (up if b is positive, down if negative).

• Let's say we want to plot (graph) the point with coordinates (4, -2).
  • Starting at (0,0) go four units to the right and then two units down.
    The point is labeled A and is in quadrant IV.
• Next, plot the point with coordinates (0,3).
  • We would not go right or left of the origin, because the x-coordinate is zero.
  • Moving up three units, we would locate the point three units above the origin on the y-axis.
    This point is labeled B in the figure below.
• Plot the point with coordinates (-2,0).
  • Go two units to the left of the origin.
    This point is labeled C in the figure below.

The line labeled as the x-axis is drawn horizontally. The line labeled as the y-axis is drawn vertically. The axes have 5 tick marks in each direction. On the x-axis, the tick marks to the right of the origin are labeled 1 through 5 and the tick marks to the left of the origin are labeled -1 through -5 as they get farther from the origin. On the y-axis, the tick marks above the origin are labeled 1 through 5 going up and -1 through -5 going down as they get farther from the origin. Point A is located four units to the right of the vertical axis and two units below the horizontal axis. Point B is located on the vertical axis three units above the horizontal axis. Point C is located on the horizontal axis two units to the left of the vertical axis. Point E is located five units to the left of the vertical axis and four units above the horizontal axis. Point F is located on the horizontal axis five units to the right of the vertical axis.

There are two additional points labeled in the figure above. We can determine the coordinates of these points by examining the numbers on the x and y axes. Point E has coordinates (-5, 4) because we can arrive there after going five units to the left of the origin and then four units up. Point F has coordinates (5,0) because it is located five units to the right of the origin, without moving up or down from there.

There may be situations where not all coordinates are integers. For example, if you have a coordinate $2\frac{2}{3}$ that needs to be plotted. We need to approximate the location to the best of our ability.

Why is placing coordinates in the correct place and understanding how to plot ordered pairs important? As we move toward solving equations with ordered pairs, this knowledge is critical.