Search results
Results From The WOW.Com Content Network
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
Perpendicular is also used as a noun: a perpendicular is a line which is perpendicular to a given line or plane. Perpendicularity is one particular instance of the more general mathematical concept of orthogonality ; perpendicularity is the orthogonality of classical geometric objects.
Here, p is the (positive) length of the line segment perpendicular to the line and delimited by the origin and the line, and is the (oriented) angle from the x-axis to this segment. It may be useful to express the equation in terms of the angle α = φ + π / 2 {\displaystyle \alpha =\varphi +\pi /2} between the x -axis and the line.
Perpendicular regression fits a line to data points by minimizing the sum of squared perpendicular distances from the data points to the line. Other geometric curve fitting methods using perpendicular distance to measure the quality of a fit exist, as in total least squares. The concept of perpendicular distance may be generalized to
the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines and calculating the distance between them. Since the lines have slope m, a common perpendicular would have slope −1/m and we can take the line with equation y = −x/m as a common perpendicular ...
The perpendicular bisectors of all chords of a circle are concurrent at the center of the circle. The lines perpendicular to the tangents to a circle at the points of tangency are concurrent at the center. All area bisectors and perimeter bisectors of a circle are diameters, and they are concurrent at the circle's center.
In a 1981 paper, N. G. de Bruijn investigated special cases of this construction in which the line arrangement consists of sets of equally spaced parallel lines. For two perpendicular families of parallel lines this construction gives the square tiling of the plane, and for three families of lines at 120-degree angles from each other ...