Cartesian plane
Topic Notes
Cartesian Coordinates System
The Cartesian plane was created by René Descartes to help people identify where something was located on a map or a graph. It uses a relationship between two variables. What are the elements to a Cartesian Coordinates System? Let's find out!
X and Y Axis
The main way that the Cartesian Coordinates System allows you to locate something is through its x and y axis. The x axis is what you call the left-right direction of the plane. A way to help you remember this is that "x" is a cross. Therefore, x goes "across" on the Cartesian plane. The y axis is what you call the up-down direction. A Cartesian plane will always have both the x and y axis.
When you write down a pair of coordinates to help other people locate something on a plane, you'll have to write it in a specific way. Keep in mind that it always comes in a pair since there's the x and y axis that you'll have to consider. This is also called an ordered pair.
There is a specific way you're supposed to write them and it's that you write the horizontal distance before the vertical one. Therefore, an ordered pair looks like this: (x, y).
You may come across the terms "axis of ordinates" and "axis of abscissae". The ordinate simply refers to the vertical portion of an ordered pair, that is, the y axis. The abscissae refers to the horizontal part of a coordinate, this is, the x axis.
Quadrants
A Cartesian plane's x and y axis divides up the plane into four quadrants. Quadrant I is located where x and y is positive (the top right corner of the plane). Quadrant II is where x is negative but y is positive (the top left corner of the plane). Quadrant III is where both x and y are negative (the bottom left corner). Lastly, quadrant IV is where x is positive and y is negative (the bottom right corner).
You may be asked to identify which quadrant a set of coordinates lie in, or be told that an ordered pair is in a certain quadrant. Let's try out some practice problems to see how coordinates work on a Cartesian plane.
Example problems
Question 1
What are the coordinates of each point shown on the coordinate grid?
![find coordinates of points on Cartesian plane](https://dcvp84mxptlac.cloudfront.net/diagrams2/MATH7-5-1-X-1.png)
Solution:
A=(ordinate, abscissa)= (x,y)= (6,8)
B=(ordinate, abscissa)= (x,y)= (-6,2)
C=(ordinate, abscissa)= (x,y)= (4,-4)
Question 2
Predict in which quadrant each of the following points will lie. Then, plot the points of a coordinate grid: A (4,-1), B (-7,3), C (-2,-5), D (0,2), E (-5,0)
Solution:
![Determine which quadrant the points will lie Q1,2,3,4](https://dcvp84mxptlac.cloudfront.net/diagrams2/determine-which-quadrant-the-points-will-lie-q-1-2-3-4.jpg)
![The signs of x and y coordinates to determine where the points lie](https://dcvp84mxptlac.cloudfront.net/diagrams2/the-signs-of-x-y-coordinates-to-determine-where-the-points-lie.jpg)
![Predict where the points lie and plot on coordinate grid](https://dcvp84mxptlac.cloudfront.net/diagrams2/predict-which-quadrants-the-points-will-lie-and-plot-the-points-on-coordinates-grid.jpg)
Question 3
Maggie walks to the pool every evening. Her house lies at H(-9,0) and the pool lies at P (9,0)
Join the pair of coordinate with a straight line segment. What is the total distance from her house to the pool? Each grid line/square represents 1km.
Solution:
![Plot the location of where Maggie lives and the swimming pool](https://dcvp84mxptlac.cloudfront.net/diagrams2/plot-the-location-of-where-maggie-lives-and-the-swimming-pool.jpg)
18 squares
18km
You can see how coordinates change as you move a point around on a Cartesian plane here on this online diagram. Watch as the x and y values change depending on where you point is!