Mathematics » Introducing Graphs » Use the Rectangular Coordinate System

Identifying Points on a Graph

Identifying Points on a Graph

In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the x-coordinate of a point on a graph, read the number on the x-axis directly above or below the point. To identify the y-coordinate of a point, read the number on the y-axis directly to the left or right of the point. Remember, to write the ordered pair using the correct order \(\left(x,y\right).\)

Example

Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 2, 4” is labeled C. The point “ordered pair -3, 3” is labeled A.  The point “ordered pair -1, -3” is labeled B. The point “ordered pair 4, -4” is labeled D.

Solution

Point A is above \(-3\) on the \(x\text{-axis},\) so the \(x\text{-coordinate}\) of the point is \(-3.\) The point is to the left of \(3\) on the \(y\text{-axis},\) so the \(y\text{-coordinate}\) of the point is \(3.\) The coordinates of the point are \(\left(-3,3\right).\)

Point B is below \(-1\) on the \(x\text{-axis},\) so the \(x\text{-coordinate}\) of the point is \(-1.\) The point is to the left of \(-3\) on the \(y\text{-axis},\) so the \(y\text{-coordinate}\) of the point is \(-3.\) The coordinates of the point are \(\left(-1,-3\right).\)

Point C is above \(2\) on the \(x\text{-axis},\) so the \(x\text{-coordinate}\) of the point is \(2.\) The point is to the right of \(4\) on the \(y\text{-axis},\) so the \(y\text{-coordinate}\) of the point is \(4.\) The coordinates of the point are \(\left(2,4\right).\)

Point D is below \(4\) on the \(x-\text{axis},\) so the \(x\text{-coordinate}\) of the point is \(4.\) The point is to the right of \(-4\) on the \(y\text{-axis},\) so the \(y\text{-coordinate}\) of the point is \(-4.\) The coordinates of the point are \(\left(4,-4\right).\)

Example

Name the ordered pair of each point shown:

The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The point “ordered pair 3, 0” is labeled C. The point “ordered pair 0, 1” is labeled D.  The point “ordered pair -4, 0” is labeled A. The point “ordered pair 0, -2” is labeled B.

Solution

Point A is on the x-axis at \(x=-4\).The coordinates of point A are \(\left(-4,0\right)\).
Point B is on the y-axis at \(y=-2\)The coordinates of point B are \(\left(0,-2\right)\).
Point C is on the x-axis at \(x=3\).The coordinates of point C are \(\left(3,0\right)\).
Point D is on the y-axis at \(y=1\).The coordinates of point D are \(\left(0,1\right)\).

[Attributions and Licenses]


This is a lesson from the tutorial, Introducing Graphs and you are encouraged to log in or register, so that you can track your progress.

Log In

Share Thoughts