!'"' 



.1 \.l/.rr/C GEOMETRY 



[Cii. V. 



E.g.* find tho (list tin- point l\=.cl. ._! > from the 



=0 ..... 1. 



Let line (1) be the locus 



<>!' .--illation (1), and /', ! 

 the given point. Through 

 l\ draw the line ( J ) par- 

 allel to line (1), also draw 

 QP l perpendicular to line 

 < l ). OR l ( = p l ) perpen- 



dicular t<> line (1), and 



=^ 3 ) perpendicular to line (2). Then d = QP l =p^pi> 

 The equation of a line parallel to line (1) is of the form 

 3* + 4y + & = 0; this will represent line (2) itself if / !> 

 so determined that the line shall pass through the point 



!=, , .e., 

 The equation of line (2) is then 



.e. 



... (2) 



Therefore [by Art. 58, (3) or (4)] 



12 7 

 hence the requ red distance is d=QP l = - = 1. 



Similarly, in general, to find the distance of any giv.-n 

 point P 1 = (a? 1 , yj) from any given line 



let line (1) be the locus of equation (1) and let P l be the 

 given point. The equation of a line parallel to ( 1 ; 5* of 

 the form Ax -I lij + K=0, this will be the line (2; if 



