1 – Dimensional shapes are those which require only one coordinate axis to represent them. For example, a Point can be termed as 1 - D. 2 - D shapes can be further categorized as conic sections, polygons and lines. These shapes can be graphed by just using two coordinate axes. Conics can further be classified in forms like a Circle, ellipse, parabola and Hyperbola. Polygons comprise of figures that are bounded by straight edges like triangle, quadrilateral (square, rectangle, parallelogram, rhombus and trapezium), pentagon, hexagon, heptagon, octagon and so on. We also can draw a straight geometrical line. All these shapes have varying features like length, area, diagonal, edge, curvature, radius, angles etc. Generally we use x and y coordinate axes to plot 2 – D shapes.
When we talk about 3 - D shapes we actually mean the figures like Solid sphere, hollow Sphere, cylinder, frustum, cone, cube, cuboid etc. There can be several other such shapes. These shapes require 3 coordinate axes to graph them. Practically 3 – D look is possible to be drawn on a plane paper using the three axes: x – axis, y – axis and z – axis. Equations of 2 – D and 3 – D shapes differ in sense that 3 – D shapes need three variables to represent them and for 2 – D shapes we would require 2 variables. A 3 – D plane would require atleast 3 points in space for its representation. A line is considered as a collection of infinite number of 1 – D Collinear Points.