58 CHAPTER 1 Graphs 30. Show that the points ( ) ( ) = − = − A B 2, 0 , 4, 4 , and ( ) = C 8, 5 are the vertices of a right triangle in two ways: (a) By using the converse of the Pythagorean Theorem (b) By using the slopes of the lines joining the vertices 31. Show that the points ( ) ( ) = = A B 2, 5 , 6, 1 , and ( ) = − C 8, 1 lie on a straight line by using slopes. 32. Show that the points ( ) ( ) = = A B 1, 5 , 2, 4 , and −( ) = C 3, 5 lie on a circle with center ( ) −1, 2 . What is the radius of this circle? 33. The endpoints of the diameter of a circle are ( ) −3, 2 and ( ) − 5, 6 . Find the center and radius of the circle. Write the general equation of this circle. 34. Find two numbers y such that the distance from ( ) −3, 2 to ( )y 5, is 10. 35. Graph the line with slope 2 3 containing the point ( ) 1, 2 . 36. Make up four problems that you might be asked to do given the two points ( ) −3, 4 and ( ) 6, 1 . Each problem should involve a different concept. Be sure that your directions are clearly stated. 37. Describe each of the following graphs in the xy-plane. Give justification. (a) = x 0 (b) = y 0 (c) + = x y 0 (d) = xy 0 (e) + = x y 0 2 2 The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. 1. Suppose the points ( ) − − 2, 3 and ( ) 4, 5 are the endpoints of a line segment. (a) Find the distance between the two points. (b) Find the midpoint of the line segment connecting the two points. In Problems 2 and 3, graph each equation by hand by plotting points. Use a graphing utility to approximate the intercepts and label them on the graph. 2. − = x y 2 7 21 3. = − y x 5 2 In Problems 4–6, use a graphing utility to approximate the real solutions of each equation rounded to two decimal places. All solutions lie between 10 − and 10. 4. − − + = x x x 2 2 1 0 3 2 5. − − = x x5 8 0 4 2 6. − + − = + − x x x x 7 2 3 3 3 2 7. Use ( ) = − P 1, 3 1 and ( ) = − P 5, 1 2 . (a) Find the slope of the line containing P1 and P .2 (b) Interpret this slope. 8. Sketch the graph of = y x 2 . 9. List the intercepts and test for symmetry: + = x y 9 2 . 10. Write the slope–intercept form of the line with slope −2 containing the point ( ) − 3, 4 . Graph the line. 11. Write the general form of the circle with center ( ) − 4, 3 and radius 5. 12. Find the center and radius of the circle + + − − = x y x y 4 2 4 0 2 2 . Graph this circle. 13. For the line + = x y 2 3 6, find a line parallel to it containing the point ( ) − 1, 1 . Also find a line perpendicular to it containing the point ( ) 0, 3 . Chapter Test In Problems 28 and 29, find the center and radius of each circle. Graph each circle by hand. Determine the intercepts of the graph of each circle. 28. + − + − = x y x y 2 4 4 0 2 2 29. + − + = x y x y 3 3 6 12 0 2 2
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