By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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Recall the fact that the bisector of an interior angle divides the opposite side into parts proportional to the other two sides. 53. In Ex. 52 find the point in which the bisector of the exterior angle at C meets A B. Given A'(1, - 3) and B ( 4, 1), find all points P meet·ing the following conditions, drawing the complete figure in each case : 54. P(3, k), given that AP is perpendicular toPE. 55. P(5, lc), given that AP is perpendicular toPE. Explain any peculiar feature that is found in connection with Ex.

5. y 8 +y2 -12y=0. 2. x 2 = xy. 3. x 2 + xy = 0. 4 y(x2+y~ • 36 y. 6. (x - 4/ = (y + 2) 2• '7_; (x - Yl = 9. 8 2 3 2x2+3xy • X + y = •2 x+y 9. If we divide both members of the cubic equation (x- y) (x2 - 6) = (x- y)x by X - y, we have the equation x 2 - 6 = x. How do the graphs of the two equations differ? 10. Show that the graph of the equation xy = 0 consists of the x axis and the y axis. 11. Draw the graph of the equation (x2 + y 2) 2 - 9 x2 = 9 if. 53 INTEHSECTIONS OF GRAPHS 55. Intersections of Graphs.

3,3),(4,1). ''4. (4,-2),(-1, 1). 5. (1, a), (a, 1). 6. (0, 0), (1, 1). Determine, witlwut writing, tlte slopes of lines perpendicular to the lines througl~ the following pairs of points : 7. (2, 4), (4, 2). 8. (1, 3), (2, 5). 9. (6, 4), (0, 1). 11. (0, 2), (0, a). 10. (3, 3), (4, 4). i 12. ( 4, 0), (a, 0). 13. Find the angle of inclination of the line through (3, 1) and(- 2,- 4). 14. The inclination of the line through (3, 2) and (- 4, 5) is supplementary to that of the line through (0, 1) and (7, 4).