We will be identifying the location of a point in a plane (like a piece of paper or map) by first constructing two number lines called axes.
- To make things easier for us, we will be drawing the axes perpendicular to each other (at 90 angles).
- One axis will be drawn horizontally and labeled as the x-axis.
- The other will be drawn vertically and labeled as the y-axis.
- We will intersect these axes at the point where zero is located on each of them (as shown below).
- We will refer to this point of intersection as the origin and give it coordinates (0,0), since the number zero will be the reference number on each axis.
Image Description: The line labeled as the x-axis is drawn horizontally. The line labeled as the y-axis is drawn vertically. These lines cross at the point labeled as the origin. 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. The quadrants are labeled with quadrant I (Roman numeral one) being the upper right region, quadrant II (Roman numeral two) being the upper left region, quadrant III (Roman numeral three) being the lower left region, and quadrant IV (Roman numeral four) being the lower right region. A point labeled (4,2) is drawn four units to the right and two units up from the origin. A point labeled (-3,4) is drawn three units left and four units up from the origin. A point labeled (-4,0) is drawn four units to the left of the origin on the x-axis. A point labeled (0,-5) is drawn five units below the origin on the y-axis.
For every point in the plane, we will identify the location using an ordered pair of the form (x,y).
- The first coordinate, the x-coordinate, will refer to the number which corresponds with the point's horizontal location as determined by the number on the x-axis. (The x-coordinate is somewhat like the east-west number.)
- The second coordinate, the y-coordinate, will refer to the number which corresponds with the point's vertical location as determined by the number on the y-axis. (The y-coordinate is somewhat like the north-south number.)
- We will always be writing the ordered pairs with the x-coordinate first and the y-coordinate second.
- Quadrant I: Both x and y-coordinate are positive.
- Quadrant II: x-coordinate is negative and y-coordinate is positive.
- Quadrant III: Both x and y-coordinate are negative.
- Quadrant IV: x-coordinate is positive and y-coordinate is negative.
The coordinates are always placed inside parentheses with a comma separating the x-coordinate from the y-coordinate.
Notice that a point on the x-axis will always have a y-coordinate of zero. A point on the y-axis will always have an x-coordinate of zero.
Instructions: In the figure above, the point with coordinates (4,2) is located in quadrant I. The point with coordinates (-3,4) is located in quadrant II. The point with coordinates (-4,0) is located on the x-axis. The point with coordinates (0, -5) is located on the y-axis. Determine the quadrant for the following ordered pairs.
Understanding how to determine the location of coordinates and ordered pairs will help you plot points correctly.