42 ANA L YTIC GEOMSTR Y [Ca. 1 1 1 



12. KxpreM by an equation that the point (h, k) is equidistant frm 

 (-1,1) and (1,2); from (1, 2) and (1, 2), Th,-,, slum that the point 

 (|,0) is equidistant from (~1. !).(!. J). ami (1,~2). 



13. Prove anuhtirally tliat the middle point of the hypotenuse of 

 a right triangle is equidistant from the three vertices. 



14. Three vertices of a parallelogram are (1, 2), (-5, -8), and (7, ~6) ; 

 what is the fourth vertex? 



15. The center of gravity of a triangle is at the point in which the 

 medians intersect Find the center of gravity of the triangle whose 

 vertices an* ( J. 8 ). (4, ~5), and (3, -6). (cf. Ex. 8, p. 40.) 



16. The line from (x,, y,) to (x r y,) is divided into five equal parts ; 

 find the points of division. 



17. Prove analytically that the two straight lines which join the 

 ini<l'lle points of the opposite sides of a quadrilateral mutually bisect 

 each other. 



18. Prove that (1, 5) is on the line joining the points (0, 2) and (2, 8), 

 and is equidistant from them. 



19. If the angle between the axes is 30, find the perimeter of the 

 triangle whose vertices are (2, 2), (~7, ~1), and (-1, 5). Plot the figure. 



20. Show analytically that the line joining the middle points of two 

 sides of a triangle is half the length of the third side. 



21. A point is 7 units distant from the origin and is equidistant from 

 the points (2, 1) and (-2, ~1) ; find its coordinates. 



22. Prove that the points (a, b + c), (6, c + a), and (c, a 4- 6) lie on 

 the same straight line. (cf. Ex. 2, p. 37.) 



