I in '.m 



Let /./., > the straight li 

 l.-t li.- (lerpendii-ular from 

 .11 U|M.II it ( oy-p) make 

 ingles a and ft respectively 

 \\itii tlie axes, and let Pm 

 /) be any point 01 / / 



nliuatr Ml* ; then, 

 by Art. 



OJ/cos a -I- MP CM ft - ON, 



IT co* a + y co* = /, 

 required equation. 

 If w is the angle between the axes, then ft 



117 

 equa nought. 



[20] 



a, 



equation [ -JO] may be \\rittnt *coa+yco*(a>-a)=;>. 

 If a> - ^, thru tlit* equation reduces to x co* a +y in a/>, 

 \\hi- ii agrees with equation [13]. 



EXERCISES 



1 The axes being inclined at the angle 60, find the inclination of 

 the line y 



2. The axes being inclined at the angle -, find the angles at which 

 the lines 3y + 7x-l=0 and * + y + 2 = cross the x-axis. 



3. Find the angle between the lines in exercise 2. 



4. The center of an equilateral triangle of side 6 is joined by *tr. 

 linen to the vertices. If two of these lines are taken as coordinate axes, 



the coordinates of the vertices, and the equations of the side*. 



>ve that for every value of w, the lines z + y = c andr-jr = </ 

 perpendicular to each other. 



The angles and ft are the Hirrftio* amylft of the line O.V. and their 

 i are the <ttrtrti* c*mr* of that line. 



