In the figure, point A' is on ray CA and point B' is on ray CB. Suppose |CA| = a and |CA'|= 6/a. Also |CB| = 2 and |CB'| = 3. If |A'B'| = c, what is |AB|?
Show your work and give (brief) reasons.
Answer: |AB| = ___________
Work:
Let ABCD be a trapezoid, with side AB parallel to CD.
Suppose that diagonal AC intersects diagonal BD at P and line BC intersects DA at Q.
Also, the line through P parallel to AB intersects BC at G and DA at H.
The length of AB = 4 and the length of CD = 1. (The figure is not to scale.)
For each question, write the answer in the blank space, but show your work below. (This is not a proof; just show how you solved it.)
(a) Find the ratio |GC|/|GB|. _________________
(b) Find the ratio |QC|/|QB|. _________________
(c) Find the ratio |DP|/|DB|. _________________
(d) Find the ratio |BG|/|BQ|. _________________
(e) Extra: No further computation necessary if you have answered a-d: Write the barycentric coordinates of P with respect to ABQ _________________