Alt A I. Yin t.'KnMKTKY [Cii. V. 



4. Fin.l the distance of the point (a, b) from th,- lin,. ' --? = !. 



a 



5. Find the distance of the intersection of the two lines, y+ 4 r 

 ami :>x=y-2, from the line 2y -7 = 9. On \\hi.-h side of the latter 

 line is the poii> 



6. Fniil the distance of the point of intersection of the lines 



2z-5y=ll and 4z = 3y + i:> from the line 1 x + -^ - 0. On 



which side of the latter line is the point? IM.it tin- figure. 



7. How far is the point (~6, -1) from 3y=7z+8? On which si 



8. llv th- method of Art. 'H. timl the distance of the origin fn.m 

 tin- lin.- :.x-2y=7: al>o from tin- linr A x + By + C = <>. Check the 

 n-Miln l.y Art. 58 (:{). 



9. Find the distance of the point (~4, -5) from the line joining the 

 t\\o {tointo (3, -1) and (~4, 2). On which side is it? 



10. Find the distance of the point (r r y,) from the line y mx -f /. 



11. Find tin- altitudes of the triangle formed by the lines whose equa- 

 tions are x + y+ 1 = 0, 3ar + 5y + 11 = 0, and z + 2y + 4 = <). Ch.M-k 

 the result by finding the area of the triangle in two ways. 



12. Show analytically that the locus of a point which moves so that 

 the sum of its distances from two given straight lines is constant is itself 

 a straight lm-. 



13. Express by an equation that the point P l = (x r y,) is equally 

 distant from the two lines 2x y= 11 and 4x = .'Jy-f two 

 answers.) Should P, move in such a way as to be always equidistant 

 from these two lines, what would be the equation of its locus ? 



14. Find, by the method of exercise 13, the equations of the bisectors 

 of the angle formed by the lines 3 x + 4 y = 12 and 4 x + 3 y = 24. 



65. Bisectors of the angles between two given lines. Tin- 

 liisrrtnr of an angle is the locus of a point which m 

 so that it is always equally distant (numerically) from the 

 > of the angle. From this property its equation may 

 v be found. 

 / /.. find the equations of the bisectors of the angles 



between the lines 



3* + 4y-l=0, ... (1) 



and 



