By Lewis Parker Siceloff, George Wentworth and David Eugene Smith

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3). 9. 2). 8. 2). 10. )· c Find the point which divides eaclt of these line segments in the rcitio stated, drawing the figure in each case : 11. (2,1)to(3,-9); 4:1. 12. (5, - 2) to (5, 3); 2: 3. 13. (-4, 1) to (5, 4); -5:2. ~, 14. (8, 5) to ( -13, - 2); 4: 3. Find the two trisection points of each of these line segments, the end points being as follows : \_ 15. (-1,2),(-10,-1). 16. (11,6),(2,3). 17. (7,8), (1,-6). 18. Find the mid points of the sides of the triangle the vertices of which are (7, 2), ( -1, 4), and (3, - 6), and draw the figure.

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). 15. If P (5, 9) is on a circle whose center is (1, 6), find the radius of the circle and the slope of the tangent at P. 16. The points (8, 5) and (6,- 3) are equidistant from (3, 2). 17. Given A(2, 1), B(3,- 2), and C(- 4, -1), show that the angle BA C is a right angle. 18. The line through (a, b) and (c, cl) is perpendicular to the line through (b, -a) and (cl, -c). · ,, 19.

Find by a graph the volume of the greatest cylinder that can be inscribed in a sphere of radius 10 in. 36. , A~P x Q and BQ = 5 mi. A pumping station P is to be built on the river to supply both towns with water. Express in terms of x the total cost C of laying the pipes at $600 a mile B for AP and $1000 a mile for PB, plot the equation, and estimate the most economical position for the pumping station. 37. Two sources of heat, A and B, are 10ft. apart, and A gives out twice as much heat as B. If P is on the line AB and is x feet from A and x' feet from B, and receives 50jx2 units of heat from A and 25 jx' 2 units of heat from R, express the total number H of units of heat received by P from both A and B, draw" the graph of the equation, and find the coolest position for P between A and B.