Skip to ContentGo to accessibility pageKeyboard shortcuts menu
OpenStax Logo
Algebra 1

Find Coordinates: Mini-Lesson Review

Algebra 1Find Coordinates: Mini-Lesson Review

Search for key terms or text.

Mini Lesson Question

Question #3: Find Coordinates

Which point has coordinates  ( 3 , 4 ) ?


  1. Point Z
  2. Point Y
  3. Point W
  4. Point X
A Cartesian plane with four labeled points: Z (purple) at (-4, 3), W (red) at (-3, 4), X (blue) at (3, -4), and Y (green) at (4, -3).

Identifying Coordinates of a Point on a Graph

In the rectangular coordinate system, every point is represented by an ordered pair. The first number in the ordered pair is the x x -coordinate of the point, and the second number is the y y -coordinate of the point. An ordered pair, ( x , y ) ( x , y ) , gives the coordinates of a point in a rectangular coordinate system. The first number is the x x -coordinate. The second number is the y y -coordinate. The phrase “ordered pair” means the order is important. What is the ordered pair of the point where the axes cross? At that point, both coordinates are zero, so its ordered pair is ( 0 , 0 ) ( 0 , 0 ) . The point  ( 0 , 0 ) ( 0 , 0 ) has a special name. It is called the origin.

We use the coordinates to locate a point on the x y x y -plane. Let’s plot the point  ( 1 , 3 ) ( 1 , 3 ) as an example. First, locate 1 on the x x -axis and lightly sketch a vertical line through x = 1 x = 1 . Then, locate 3 on the y y -axis and sketch a horizontal line through y = 3 y = 3 . Now, find the point where these two lines meet—that is the point with coordinates ( 1 , 3 ) ( 1 , 3 ) .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the \(x\)-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the \(x\)-axis, the other parallel to the \(y\)-axis, meet perpendicularly at 1, 3. The dotted line parallel to the \(x\)-axis intercepts the \(y\)-axis at 3. The dotted line parallel to the \(y\)-axis intercepts the \(x\)-axis at 1.

Notice that the vertical line through  x = 1 x = 1 and the horizontal line through  y = 3 y = 3 are not part of the graph. We just used them to help us locate the point ( 1 , 3 ) ( 1 , 3 ) .

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 x -coordinate of a point on a graph, read the number on the x x -axis directly above or below the point. To identify the y y -coordinate of a point, read the number on the y y -axis directly to the left or right of the point. Remember, when you write the ordered pair, use the correct order, ( x , y ) ( x , y ) .

Try it

Try It: Identifying Coordinates of a Point on a Graph

Name the ordered pair of each point shown in the rectangular coordinate system.

A coordinate plane with six labeled points: A at (−3, 3), B at (−2, −3), C at (3, 4), D at (4, −4), E at (0, −2), and F at (2, 1).

Check Your Understanding

Which point has coordinates ( 4 , 3 ) ( 4 , 3 ) ?

A Cartesian plane with four labeled points: Z (purple) at (-4, 2), W (red) at (-2, 4), X (blue) at (2, -4), and Y (green) at (4, -2).

Multiple Choice:

  1. Point W W

  2. Point Z Z

  3. Point X X

  4. Point Y Y

Video: Points on the Coordinate Plane

Khan Academy: Points on the Coordinate Plane

Watch this video to see how you can use a coordinate plane to plot points and to identify the coordinates of a point plotted on a coordinate plane.

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information
  • If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

  • If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.