Distance from a point to a line the perpendicular "R". Draw the vertical line through "P" and label its intersection with the given line "S". At any point "T" on the line, draw a right triangle "TVU" whose sides are horizontal and vertical line segments with hypotenuse "TU" on the given line and horizontal side of length |"B"| (see diagram). The vertical side of ∆"TVU" will have length |"A"| since the line has slope -"A"/"B". ∆"PRS" and ∆"TVU" are similar triangles, since they are both right triangles and ∠"PSR" ≅ ∠"TUV" since they are corresponding angles of a transversal to the parallel lines "PS" and "UV" (both
Altitude (triangle) the tangential triangle, and the center of similitude of the orthic and tangential triangles, are on the Euler line. Trilinear coordinates for the vertices of the tangential triangle are given by For more information on the orthic triangle, see here. For any triangle with sides and semiperimeter , the altitude from side is given by This follows from combining Heron's formula for the area of a triangle in terms of the sides with the area formula (1/2)×base×height, where the base is taken as side and the height is the altitude from . Consider an arbitrary triangle with sides and with