Abelian Varieties by D. Mumford

By D. Mumford

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GUIDED PRACTICE for Examples 1 and 2 In Exercises 1 and 2, identify the segment bisector of } PQ. Then find PQ. 1 78 1. P 2. l P M N 5x 2 7 11 2 2x P P M COORDINATE PLANE You can use the coordinates of the endpoints of a segment to find the coordinates of the midpoint. For Your Notebook KEY CONCEPT The Midpoint Formula The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints. If A(x1, y1) and B(x2, y 2) are points in a coordinate plane, then the midpoint M of } AB has coordinates x1 1 x 2 y 1 1 y 2 , } 2.

35. 38. 41. 24 22 230 ★ 220 36. 0 2 210 39. 0 37. 28 26 24 22 29 26 0 2 4 40. 23 0 3 220 210 0 28 24 26 10 20 22 30 0 MULTIPLE CHOICE The endpoints of } LF are L(22, 2) and F(3, 1). The endpoints of } JR are J(1, 21) and R(2, 23). What is the approximate difference in the lengths of the two segments? 24 42. 96 } } SHORT RESPONSE One endpoint of PQ is P(22, 4). The midpoint of PQ is M(1, 0). Explain how to find PQ. COMPARING LENGTHS The endpoints of two segments are given. Find each segment length.

Explain. A D Chapter 1 Essentials of Geometry F C B W 63 50 12. ERROR ANALYSIS In the figure at the right, 16. JK 26 11. Find DE. 42 30 12 N C F FINDING LENGTHS In the diagram, points V, W, X, Y, and Z are collinear, VZ 5 52, XZ 5 20, and WX 5 XY 5 YZ. Find the indicated length. 21. WX 22. VW 23. WY 24. VX 25. WZ 26. VY 27. ★ V W X Y MULTIPLE CHOICE Use the diagram. What is the length of } EG ? 6x 6 F x G ALGEBRA Point S is between R and T on } RT. Use the given information to write an equation in terms of x.

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