18 CHAPTER 1 Graphs In Problems 39–42, find the length of the line segment. Then find the midpoint of the line segment. Assume that the endpoints of each line segment have integer coordinates. 39. 18 218 26 6 40. 6 26 212 12 41. 12 212 212 12 42. 12 212 26 6 Applications and Extensions 43. Find all points having an x-coordinate of 3 whose distance from the point ( ) − − 2, 1 is 13. (a) By using the Pythagorean Theorem (b) By using the distance formula 44. Find all points having a y-coordinate of −6 whose distance from the point ( ) 1, 2 is 17. (a) By using the Pythagorean Theorem (b) By using the distance formula 45. Find all points on the x-axis that are 6 units from the point ( ) − 4, 3. 46. Find all points on the y-axis that are 6 units from the point ( ) − 4, 3. 47. Plot the points ( ) = A 2, 1 and ( ) = M 5, 4 in the xy-plane. If M is the midpoint of a line segment AB, find the coordinates of B. 48. Plot the points ( ) = − A 1, 8 and ( ) = M 2, 3 in the xy-plane. If M is the midpoint of a line segment AB, find the coordinates of B. 49. The midpoint of the line segment from P1 to P2 is ( ) −1, 4 . If ( ) = − P 3, 6 , 1 what is P ?2 50. The midpoint of the line segment from P1 to P2 is ( ) − 5, 4. If ( ) = − P 7, 2, 2 what is P ?1 51. Geometry The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side (see the figure). Find the lengths of the medians of the triangle with vertices at ( ) ( ) = = A B 0, 0 , 6, 0 , and ( ) = C 4, 4 . Median A B C Midpoint 52. Geometry An equilateral triangle has three sides of equal length. If two vertices of an equilateral triangle are ( ) 0, 4 and ( ) 0, 0 find the third vertex. How many of these triangles are possible? In Problems 53–56, find the length of each side of the triangle determined by the three points P P , , 1 2 and P .3 State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) 53. ( ) ( ) ( ) = = − = − − P P P 2, 1 ; 4, 1 ; 4, 3 1 2 3 54. ( ) ( ) ( ) = − = = − P P P 1, 4 ; 6, 2 ; 4, 5 1 2 3 55. ( ) ( ) ( ) = − − = = P P P 2, 1; 0, 7 ; 3, 2 1 2 3 56. ( ) ( ) ( ) = = − = P P P 7, 2 ; 4, 0 ; 4, 6 1 2 3 57. Baseball A major league baseball “diamond” is actually a square 90 feet on a side (see the figure). What is the distance directly from home plate to second base (the diagonal of the square)? Pitching rubber Home plate 1st base 2nd base 3rd base 90 ft 90 ft 58. Little League Baseball The layout of a Little League playing field is a square 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? Source: 2018 Little League Baseball Official Regulations, Playing Rules, and Operating Policies 59. Baseball Refer to Problem 57. Overlay a rectangular coordinate system on a major league baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. (a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. s s s (continued)
RkJQdWJsaXNoZXIy NjM5ODQ=