In 6th grade, students start to learn geometrical planes and how to envision different shapes and constructions in 2D. Developing a 2D vision enables students to understand architecture and translate it, later on, into 3D representations. The coordinate plane system is hundred years old and was invented by **Rene Descartes**, and it was primarily called The Cartesian Plan. The fundamental 2D representation of shapes is constructed on coordinate planes, so let’s see what this means.

## Definition and Representation of Coordinate Planes

A coordinate plane is a two-dimensional representation formed by two intersecting, perpendicular lines. The two lines are named: X-axis being the horizontal line, Y-axis being the vertical line.

Anywhere we choose a point on the coordinate plane, that point will have two indicators (x-axis, y-axis). As we can see from the image above, the left side of the x or y-axis has negative values, therefore any number on the bottom, left-part will be a negative integer. The middle point, the intersection of the two axes is called the origin or 0.

The purpose of a coordinate plane is to allow the sketching or planning of different objects, or shapes within certain measurements. It is like a template or a canvas, a map of shapes.

## Elements Of The Coordinate Plane

A coordinate plane is built by 4 quadrants, indicated by the intersection of the two axes. As seen in the image above when X-axis intersects the Y-axis, the result is four different areas called quadrants, indicated by roman numerals:

Quadrant I: Both axes, the X-axis and Y-axis have positive numbers, in the upper right area.

Quadrant II: X-axis has negative numbers, and Y-axis has positive numbers, in the upper left area.

Quadrant III: Both axes, the X-axis and Y-axis have negative numbers, in the left bottom area;

Quadrant IV: Y-axis has negative numbers, and X-axis has positive numbers, in the right bottom area;

Coordinate: points in the coordinate plane are indicated by pair of X and Y indicators, always mapped by the (X, Y) pair.

For example, let’s take point A:

On the coordinate plane, point A is given by the pair (2, 3).

Try to indicate the following points on the coordinate plane. Remember that the point is given in the order X and Y (X, Y).

A1 (3, 4) D (5, 6)

B ( -1, 2) E ( -4, 1)

C ( – 5, – 2) F ( 0, 0)

We can also represent all the points on the X-axis with (X, 0), while all the points on the Y-axis are represented by (0, Y).

Do you understand the geometry of the coordinate plane system? You can test the infinite aspect of the coordinate plan system online, **here**.

Answer the following questions:

- In which quadrants of the coordinate plane are the following points?

- A (2, – 2 )
- B (4, – 5)
- C (- 2,-3)
- D (- 1, 1)

- Which of the following points lie on the x-axis? Indicate your answers by drawing the coordinate plane and the given coordinates:

- A ( – 6, 0)
- B (0, 2)
- C ( -3, 0)
- D ( 5, 0)

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