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Dallas ( / ˈdæləs /) is a city in the U.S. state of Texas and the most populous city in the Dallas–Fort Worth metroplex, the most populous metropolitan area in Texas and the fourth-most populous metropolitan area in the United States at 7.5 million people. [11] It is the most populous city in and seat of Dallas County with portions extending into Collin, Denton, Kaufman, and Rockwall ...
North Dallas is an area of numerous communities and neighborhoods in Dallas, Texas (United States). The phrase "North Dallas" is also sometimes used to include any suburb or exurb north of Dallas proper within the metropolitan area. The majority of North Dallas is located in Dallas County, while a small portion is located in Collin and Denton counties. North Dallas generally includes areas of ...
Farmers Branch, officially the City of Farmers Branch, is a city in Dallas County, Texas, United States. It is an inner-ring suburb of Dallas and is part of the Dallas–Fort Worth metroplex. Its population was 35,991 at the 2020 census. [7]
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, [1] the term is also frequently used metaphorically to mean a ...
Earth mover's distance. In computer science, the earth mover's distance ( EMD) [1] is a measure of dissimilarity between two frequency distributions, densities, or measures, over a metric space D . Informally, if the distributions are interpreted as two different ways of piling up earth (dirt) over D, the EMD captures the minimum cost of ...
In Euclidean space, the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the nearest point on the plane. It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted ...