00-411. J //// -Hi. IH. II I I.ISK 



13 v means of cos a and sin a what quadrant is 

 each of the hoes: 



14 .-. uii mut be the slope of the line 4z Ay 17 in order U. 

 shall pa* > ? Has i a finite value for which thb 



.UM through the orL 



15 Determine the values of A, B, C in order that the UM 



*0 

 shall pass through the points (3, t U; [\ le.] 



16 Derive equation [0] by supposing (x t . y.) and (x r y,) to be two 

 points on the line y = mx + >>; and thence finding values for M and ft. 



17 Kind the slopes of the lines 2y-3x = 7 ami :\y 4 2x 11 

 ami thence show that these lines are perpendicular to each other. 



18. Kind cos a for each of the lines 7x + y - 9 = snl r-7y + 2 = 0. 

 ml then show thai the two liues are perpendicular to each other. 



19. Show by means of: (1) the slopes; (2) the angles; that the lines 



are all parallel. 



20. Reduce the equ;t t-y+C=0 to the normal form, 



11 xcosa + ysina=/>. Suggestion: the two equations, as 

 representing the same line, make the same intercepts on the axes. 



61. To find the angle made by one straight line with another. 

 Let the equations of the lines be 



-f /.,. . 

 :iinl ymir + l* . 



where mi^tan^, fn,=tan^ 

 aiul ^,, 0, are the angles which 

 these lines make, respec- 



itli the z-axis. Ilia S\ \ 



:! to lin.l the angle </K 

 measured frmn 11: - line (1). 







