Exam 1

  1. Question

    What is the distance between the two points p=(3,4) and q=(5,2) in a Cartesian coordinate system?

    Solution

    The distance d of p and q is given by d2 =( p1 - q1 )2 +( p2 - q2 )2 (Pythagorean formula).
    Hence d=( p1 - q1 )2 +( p2 - q2 )2 =(3-5 )2 +(4-2 )2 =2.828.
    data:image/png;base64,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