84 ANAL ) TH GEOMETRY [Cii. V. 



2. Write down the equations of the lines through the following 

 pain of points : 



(a) (3, 4) and (.V (y) (-6, 1) and (-2, ~5); 



(ft) (3, 4) and (8) ("15, -3) and (|, ^L). 



3. Write the equations of the lines which make the following inter- 

 cepts on tin- ./ and y-axes respectively. 



(a) 4 and 7; (ft) -3 and 5; (y) i and -1; (5) -| and 8 



4. What do equations [9] and [10] become if one of the given 

 points Is the origin? 



5. By drawing, in Fig. 42, a perpendicular 7M/ fnmi /' to the z-axis, 

 derive equation [10] from the .similar triangles MAP and OAB. 



6. Is equation [10] true if P is on MN but not between A and J5? 



7. Are equations [!] and [10] true if the coordinate axes are not 

 at right angles to each other? 



8. Is the point (3, 4J) on the line through the points (2, 3) and 

 i .' On which side of this line is it? Which is the negative side 



of this line? 



9. What intercepts does the line through the points (1, -6) and 

 (~3, 5) make on the axes ? 



10. The vertices of a triangle are : (4, ~5), (2, 3), and (3, -6). Find 

 the equations of the sides; also of the three medians; then find the 

 coordinates of the point of intersection of two of these medians, and 

 show that these coordinates satisfy the equation of the other median. 

 What proposition of plane geometry is thus proved? 



11. Find the tangent of the angle (the " slope," cf. Art. 27) which 

 the line in exercise 9 makes with the z-axis. 



12. Draw the line whose equation is - + * = 1, and then find the 



- 



equations of the two lines which pass through the origin and trisect that 

 portion of this line which lies in the first quadrant. 



53. Equation of straight line through a given point and 

 in a given direction (of. Art. H ). Let P l =(x r y^ be 

 the given point, and let the direction of the line be given 

 by the angle XAP = which the line makes with the 

 ar-axis; also let P = (x, y) be any point on the given line 

 and denote the slope. ?'.*., tan 0, by /" I) raw the ordinates 



