Dowling, L. Wayland (Linnaeus Wayland), b. 1867, Turneaure, F. E. (Frederick Eugene), 1866- · New York, H. Holt and company · leaf 121
f each line. Draw the figure. 88. Distance from a line to a point. With the help of thenormal form of the equation of a straight line, it is easy to find the length of the perpen-dicular DP drawn from agiven line AB to a givenpoint P(x„ y,) (Fig. 65).Thus, let the equation ofAB, reduced to the… … Fig. 65 X COS u-\-y sin « — 2h — 0- (2) Since P is on RS, the coordinates Xj^ and y^ must satisfy (2). Hence, . Xi cos «-f ?/i sm « = 2h- (<j) Subtracting p from both members of (3), we have al cos a + ?/i sin a — p=lh —P= OM— 0K= DP. Arts. 88, 89] DISTANCE FROM A LINE TO A POINT 105 Hence the…
Geometry, Analytic
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