Coordinate Rules

Coordinate Rules are mathematical instructions that describe how points, graphs, or geometric figures change position on a coordinate plane. They work by applying an algebraic rule to each ordered pair, such as adding values for a translation, multiplying coordinates for a dilation, or switching coordinates and changing signs for certain rotations and reflections. Students and researchers use coordinate rules to represent transformations, analyze symmetry, connect algebra with geometry, and predict the locations of transformed points. They also provide a precise framework for graphing functions and modeling spatial relationships in mathematics and related scientific fields.

Coordinate Rules - Related Videos

Education

JoVE Core - Chemistry

Exceptions to the Octet Rule

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2020

Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories: Odd-electron molecules have an odd number of valence electrons and therefore have an unpaired electron. Electron-deficient molecules have a central atom with fewer electrons than needed for a noble gas configuration. Hypervalent molecules have a central atom that has more electrons than needed for a noble gas configuration. Odd-electron...

Coordination Number and Geometry

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2020

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar. Coordination Number Molecular Geometry Example 2 linear [Ag(NH3)2]+ 3 trigonal planar [Cu(CN)3]2− 4 tetrahedral(d0 or d10), low oxidation...

The Aufbau Principle and Hund's Rule

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2020

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the aufbau principle, from the German word aufbau (“to build up”). Each added electron occupies the subshell of...

Coordination Compounds and Nomenclature

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2020

In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...

Lattice Centering and Coordination Number

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2020

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1. Types of Unit Cells Imagine taking a large number of identical...

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