Cartesian plane

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?

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:

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:

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!