Question 1199273: Points B(b,0) and C(c,10) are to be placed on this graph so that the distance from A to B to C to D is a minimum. Find the value of b.
Also: Point A is at (0,4) and point D is at (8,9)
PLEASE DO NOT GIVE ME THE SOLUTION OF MATHLOVER AS IT IS INCORRECT. HER ANSWER IS NOT ONE OF THE MULTIPLE CHOICE WHICH CAN BE FOUND HERE:
a) 3 4/15
b) 1 7/15
c) 2 2/25
d) 2 4/15
e) 2 7/15
Thanks!
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443)   (Show Source):
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
I don't know what answer the other tutor gave you; so I don't know if mine is different. But it is not one of the answer choices you show....
The y coordinates of A, B, C, and D in that order are 4,0,10, and 9, so the paths from A to B and from C to D are downward and the path from B to C is upward. It should be clear that the minimum distance from A to B to C to D will be when the path is always moving in the same direction left or right. Since A is (0,4) and D is (8,9), the desired path moves always left to right. So the slope of AB is negative, the slope of BC is positive, and the slope of CD is negative.
slope of AB is -4/b
slope of BC is 10/(c-b)
slope of CD is -1/(8-c)
The minimum distance from A to B to C to D will be if the slopes of AB and CD are the same and the slope of BC is the opposite.
The slope of AB is the same as the slope of CD:
 (1)
The slope of BC is the opposite of the slope of AB:
 (2)
Substitute (2) in (1):
ANSWER: b = 32/15 = 2 2/15
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