Is there a difference between a geometric shape and a geometric figure? Many writers seem to use the words "Shape" and "Figure" interchangeably, and few give definitions of these terms. Is there a difference, and if so what is it ?
 A: There are nuances one might want to distinguish between here (for example whether a different scale, orientation or position makes something into a different figure/shape), but there is no widespread and generally understood convention for how to make those distinction with a choice between "shape" and "figure".
As a writer, you should not depend on a reader understanding such differences from your choice of words, so if you need to make the distinction, you'll need to explain explicitly how you use each word.
As a reader, be extremely wary of assuming that an author is using the words with any particular distinction in mind, unless he explicitly explains that he is. At worst, you may need to reconstruct the particular definitions the author is using such that what he says makes sense.
A: The definitions suffice sometimes to tell the difference. Taken from Wikipedia and Mathwords, the following are the definitions of Shape and Figure:
From Wikipedia

A geometric shape is the geometric information which remains when location, scale, orientation and reflection are removed from the description of a geometric object.

From Mathwords

A geometric figure is any set of points on a plane or in space.

But most often they can be use differently according to context or circumstances, so being a reader it depends on the conclusive mind  of yours  and context that what does these terms mean, but prefer these if you have got nothing as information.
A: A geometric shape is determined by how intrinsic slope  and curvature of lines, and double curvature  of areas vary depending on its plane or spatial coordinates. A figure is an assembly of points and lines. 
A: Geometric figure are those which forms in a question and a part of it. And geometric shape are such as circle, rectangle, square etc.
