Proof of the Distance Formula in Three-Dimensional Spaces Viewed from the Scope of Geometry
Mahfudz Reza Fahlevi

IAIN Syaikh Abdurrahman Siddik Bangka Belitung, Indonesia

Abstract

This paper aims to present various proofs on a quick formula (distance formula) in three-dimensional space materials. One of the materials in the domain of geometry is a three-dimensional space. Geometry is one of the most essential subjects of mathematics to understand because of its many benefits. But, in school mathematics learning, the use of quick formulas in three-dimensional space materials is quite often given, this is accompanied by not being equipped with the cultivation of a strong concept understanding so that it can have a negative impact on students mathematics learning culture. As a result, it will gradually encourage students to an instant and non-constructive culture that keeps students away from honesty and responsibility. Through this paper, researchers seek to contribute to providing mathematical proofs of a quick formula so that it can be a reference for educators. The proof of the quick formula in this paper will be explained from various points of view using various materials that are still within the scope of geometry. The materials involved include the concept of similarity, the concept of area of a triangle, the concept of three-dimensional space, analytical geometry (with a Cartesian coordinate system), and vector analysis approach (vector space).

Keywords: Distance in three-dimensional spaces, Proof, Quick formula

Topic: MATHEMATICS AND SCIENCE EDUCATIONS