46. Reasoning The midpoint of T S ¯ t s bar  is the origin. Point T is located in Quadrant II. What quadrant contains point S? Explain.

47. Do you use the Midpoint Formula or the Distance Formula to find the following?
    1. Given points K and P, find the distance from K to the midpoint of K P ¯ . k p bar , .
    2. Given point K and the midpoint of K P ¯ , k p bar , comma  find KP.

For each graph, find (a) AB to the nearest tenth and (b) the coordinates of the midpoint of A B ¯ . eh b bar , .

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51. Coordinate Geometry Graph the points A(2, 1), B ( 6 , − 1 ) , b open 6 comma negative 1 close comma  C(8, 7), and D(4, 9). Draw parallelogram ABCD, and diagonals A C ¯ eh c bar  and B D ¯ . b d bar , .

    1. Find the midpoints of A C ¯ eh c bar  and B D ¯ . b d bar , .
    2. What appears to be true about the diagonals of a parallelogram?

Travel The units of the subway map below are in miles. Suppose the routes between stations are straight. Find the distance you would travel between each pair of stations to the nearest tenth of a mile.

Image Long Description

52. Oak Station and Jackson Station
53. Central Station and South Station
54. Elm Station and Symphony Station
55. Cedar Station and City Plaza Station
56. Maple Station is located 6 mi west and 2 mi north of City Plaza. What is the distance between Cedar Station and Maple Station?
57. Open-Ended Point H(2, 2) is the midpoint of many segments.
    1. Find the coordinates of the endpoints of four noncollinear segments that have point H as their midpoint.
    2. You know that a segment with midpoint H has length 8. How many possible noncollinear segments match this description? Explain.

C Challenge

58. Points P ( − 4 , 6 ) , p open negative 4 comma 6 close comma  Q(2, 4), and R are collinear. One of the points is the midpoint of the segment formed by the other two points.
    1. What are the possible coordinates of R?
    2. Reasoning R Q = 160 . r q equals , square root of 160 , .  Does this information affect your answer to part (a)? Explain.

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