Question 1199273
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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....<br>
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.<br>
slope of AB is -4/b
slope of BC is 10/(c-b)
slope of CD is -1/(8-c)<br>
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.<br>
The slope of AB is the same as the slope of CD:
{{{-4/b=-1/(8-c)}}}
{{{4c-32=-b}}} (1)<br>
The slope of BC is the opposite of the slope of AB:
{{{10/(c-b)=4/b}}}
{{{4c-4b=10b}}}
{{{4c=14b}}} (2) <br>
Substitute (2) in (1):<br>
{{{14b-32=-b}}}
{{{15b=32}}}
{{{b=32/15}}}<br>
ANSWER: b = 32/15 = 2 2/15<br>