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The Cartesian Plane - Cycle 3
| Mathematics
What is a Cartesian Plane?
The Cartesian plane is a reference system.
Example:
The Cartesian plane is divided into 4 quadrants separated by the x-axis (horizontal axis) and the y-axis (vertical axis).
Each axis is graduated with positive integers and negative integers. The centre point of the plane is 0.
What are Coordinates?
Coordinates are numbers that specify the horizontal or vertical position of a point on the Cartesian plane.
The horizontal coordinate represents the position of a point on the x-axis (horizontal axis).
The vertical coordinate represents its position on the y-axis (vertical axis).
The horizontal coordinate of the point is -3.
The vertical coordinate of the point is 1.
While the one-quadrant Cartesian plane has only positive coordinates, the Cartesian plane with 4 quadrants has both positive and negative coordinates.
Each quadrant has different positive and/or negative coordinates.
- 1st quadrant: positive horizontal coordinate, positive vertical coordinate.
- 2nd quadrant: negative horizontal coordinate, positive vertical coordinate.
- 3rd quadrant: negative horizontal coordinate, negative vertical coordinate.
- 4th quadrant: positive horizontal coordinate, negative vertical coordinate.
Examples :
What is an Ordered Pair?
An ordered pair is used to find the exact position of a point on a Cartesian plane. Write the horizontal coordinate followed by the vertical coordinate between brackets. Separate the two coordinates by a comma.
What is the Origin?
The origin is the meeting point (the intersection) of the x-axis (horizontal axis) and the y-axis (vertical axis). It is represented by the coordinates (0, 0).
Example:
How Do You Place a Point on the Cartesian Plane Using its Coordinates?
To place a point on the Cartesian plane using its coordinates, follow these steps:
- Look at the first coordinate in the ordered pair and find the line corresponding to this number on the horizontal axis.
- Look at the second coordinate in the ordered pair and find the line corresponding to this number on the vertical axis.
- Place the point where these two lines meet (intersect).
Place the point with coordinates (4, -3) on the Cartesian plane.
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Place the point with coordinates (-1, -4) on the Cartesian plane.
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How to Find the Position of a Point on the Cartesian Plane?
To find the position of a point on the Cartesian plane, follow these steps:
- Find the horizontal coordinate of the point.
- Find the vertical coordinate of the point.
- Write the ordered pair with the horizontal coordinate followed by the vertical coordinate in brackets, and separate them by a comma.
Write the position of the point on the following Cartesian plane.
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| (-2, -1) |
Write the position of the point on the following Cartesian plane.
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| (5, -5)
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