Math 444 Quiz 3

Problem 1. Compute a distance (10 Points)

In the plane, A' is on ray OA and B' is on ray OB. The lengths are |OA| = 7, |OA'| = 3/7, |OB| = 5, |OB'| = 3/5, |AB| = k, for some constant k.

• Find the distance |A'B'|. Show your reasoning briefly. (The answer should only involve k and numerical constants – no other symbols.)

Problem 2. Construct Geometric Mean (10 Points)

a) What is the definition of the geometric mean of two numbers a and b?

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b) Construct a segment CD whose length is the geometric mean of the two lengths a and b. List BRIEFLY your main steps so that one can follow what you did.

Problem 3: Construction Problem (10 points)

In this figure are 4 lines, a, b, c, d, through point O. Line c is perpendicular to a and line d is perpendicular to b. Let the line reflections in these lines be denoted by R_a, R_b, R_c, R_d.

Part A. Construct, in an efficient way, the point D1 = R_dR_c(D). Write some notes listing BRIEFLY the 2 or 3 or fewer main steps of your method.

Part B. Construct, in an efficient way, the point D2 = R_bR_a(D). Write some notes listing BRIEFLY the 2 or 3 or fewer main steps of your method.