Representing Points

In a plane, we use two coordinate axes, the x-axis and y-axis, that are perpendicular to each other to determine the location of any point in the plane.

A point in the plane can be represented as an ordered pair (a, b) of real numbers, where a is the x-coordinate and b is the y-coordinate.

Hence, a plane is called two-dimensional.

point(a,b).JPG

In space, we use three coordinate axes, the x-axis, y-axis and z-axis, (each of which is perpendicular to the other two) that meet at a point O, the origin.

A point in space can be represented as an ordered triple (a, b, c) of real numbers, where a is the x-coordinate, b is the y-coordinate and c is the z-coordinate.

Hence, space is called three-dimensional.

x1.JPG

To locate a point P(a, b, c), we can start at the origin O, move a units along the x-axis, then b units parallel to the y-axis, and then c units parallel to the z-axis.

 


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