Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T ( P ) of any point P is determined by noting that T ( A ) = A ′, T applied to the line segment AB is A ′ B ′, T applied to the line segment AC is A ′ C ′, and T respects scalar multiples of vectors based at A.

Furthermore the cyclic quadrilateral formed from the four nine-pont centers is homothetic to the reference cyclic quadrilateral ABCD by a factor of −< sup > 1 </ sup >/< sub > 2 </ sub > and its homothetic center ( N ) lies on the line connecting the circumcenter ( O ) to the anticenter ( M ) where ON = 2NM.

Prior to the demotion of beta-blockers as first line agents, the UK sequence of combination therapy used the first letter of the drug classes and was known as the " ABCD rule ".

Then, since ABCD is a rhombus, P is the midpoint of both line segments BD and AC.

It saw the Triple Intervention of 1895 as a threat to Japanese survival in East Asia and warned that the " ABCD Powers " ( Americans, British, Chinese, and Dutch ) were threatening the Empire of Japan.

The nationalists believed that the " ABCD powers " ( Americans, British, Chinese, Dutch ) were a threat to all Asians and that Asia could only survive by following the Japanese example.

American-Born Confused Desi ( ABCD ) is a term used to refer to South Asian Americans born in the United States, in contrast to those who were born overseas and later settled in the USA.

These segregations on both sides have led to the term ABCD and FOB being used.

* ABC ( medicine ), also known as ABCD, a mnemonic for steps in resuscitation

* ABCD rating, a staging system for prostate cancer

* ABCD guideline, a heuristic for detecting melanomas

* ABCD Schema, a highly-structured data exchange and access model for taxon occurrence data ( specimens, observations, etc.

* Action for Boston Community Development, Inc. ( ABCD ), a Boston, Massachsuetts based non-profit social services agency

A simple pattern is just a text string ( e. g. " ABCD "), but a complex pattern may be a large structure describing, for example, the complete grammar of a computer language.

* Robert White ( deceased 1969 ) First Director, Action for Boston Community Development ( ABCD )

Another necessary and sufficient condition for a convex quadrilateral ABCD to be cyclic is that an angle between a side and a diagonal is equal to the angle between the opposite side and the other diagonal.

The melodic structure of the presumed model ( s ) can be described as " ABCD " -- a new melodic phrase for each of its four lines.

The purpose of the American Board of Cosmetic Dentistry ( ABCD ) is the testing, analyzing, and evaluation of the services of dentists and laboratory technicians for the purpose of awarding AACD Accreditation in cosmetic dentistry.

ABCD rating, also called the Jewett staging system or the Whitmore-Jewett staging system, is a staging system for prostate cancer that uses the letters A, B, C, and D.

The ABCD method is a strategic tool applied for backcasting from the 4 sustainability principles.

For the separate nationalities, the ABCD Hierarchy, a system which ranked the 120 languages of the Soviet Union according their communicable significance, charted out a specific plan for each nationality's achievement of literacy.

Unfortunately for the average person, many seborrheic keratosis, some lentigo senilis, and even warts may have ABCD characteristics, and cannot be distinguished from a melanoma without a trained eye or dermatoscopy.

Before beginning the construction, the vertex figure ABCD is obtained by cutting each connected edge at ( in this case ) its midpoint.

Clinical diagnosis can be made with the naked eye using the ABCD guideline or by using dermatoscopy.

The quadrilateral ABCD forms a parallelogram by construction ( as opposite sides are parallel ).

The Teaneck, New Jersey-based ABCD Camp is an invitation-only basketball showcase previously attended by high-profile players including Kobe Bryant, Stephon Marbury, Tracy McGrady, LeBron James and Carmelo Anthony.

The working of the linear planimeter may be explained by measuring the area of a rectangle ABCD ( see image ).

Source: MediaWiki software, with public domain modifications to style by ABCD

Always side by Lula, she encouraged other women to participate in the Trade Union of ABCD.

The area of circle ABCD is, by definition, equal to 1.

Ajay K. Ojha argues that ABCD " is a distinctive way of speaking, as it is humorous among mainstream Asian Indians, but can be taken as offensive or challenging to Asian Indian Americans.

Of the remaining four books, two were ultimately sold to a commercial gallery in New York, one to the ABCD collection in Paris, and one other is in a private collection in Brooklyn NY.

Two points A and B are said to be harmonic conjugates of each other with respect to another pair of points C, D if ( ABCD ) = − 1, where ( ABCD ) is the cross-ratio of points A, B, C, D ( See Projective harmonic conjugates.

Clinical diagnosis of a melanocytic nevus from other nevi can be made with the naked eye using the ABCD guideline, or using dermatoscopy.

ABCD is a list of the first four letters in the English alphabet.

* ABCD ships, The first four steel ships built during the " New Navy " period of U. S. Naval history-Atlanta, Boston, Chicago and Dolphin

: area of A ′ B ′ C ′ D ′ / area of ABCD.

Two lines that are perpendicular would be denoted as ABCD.

Both cities are located in the ABCD Region, home to most of Brazil's automobile manufacturing facilities ( such as Ford, Volkswagen, Toyota, Mercedes-Benz and others ) and are among the most industrialized in the country.

Nevertheless, this would still yield profit equal ABCD from consumer Y.

As it turns out, since consumer Y's demand is twice consumer X's, ABCD = 2 x AC.

Ray transfer matrix analysis ( also known as ABCD matrix analysis ) is a type of ray tracing technique used in the design of some optical systems, particularly lasers.

In the former case, the quadrilateral is ABCD, and in the latter case, the convex quadrilateral is ABDC.

* In a cyclic quadrilateral ABCD, the incenters in triangles ABC, BCD, CDA, and DAB are the vertices of a rectangle.