Search results
Results From The WOW.Com Content Network
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.
Parallel curves of the implicit curve (red) with equation + = Generally the analytic representation of a parallel curve of an implicit curve is not possible. Only for the simple cases of lines and circles the parallel curves can be described easily. For example:
Because the lines are parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance. Given the equations of two non-vertical parallel lines
An example of coplanar points. Two lines in three-dimensional space are coplanar if there is a plane that includes them both. This occurs if the lines are parallel, or if they intersect each other. Two lines that are not coplanar are called skew lines.
Parallel lines are mapped on parallel lines, or on a pair of points (if they are parallel to ). The ratio of the length of two line segments on a line stays unchanged. As a special case, midpoints are mapped on midpoints. The length of a line segment parallel to the projection plane remains unchanged. The length of any line segment is shortened ...
The number of vertices is smaller when some lines are parallel, or when some vertices are crossed by more than two lines. [4] An arrangement can be rotated, if necessary, to avoid axis-parallel lines. After this step, each ray that forms an edge of the arrangement extends either upward or downward from its endpoint; it cannot be horizontal.
The intersection point of two polar lines (for example, ,) is the pole of the connecting line of their poles (in example: ,). Focus and directrix of the parabola are a pole–polar pair. Remark: Pole–polar relations also exist for ellipses and hyperbolas.
For example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. [1] A cleaver of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at