SOLUTION: 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. Note: point A is at (0,4) and point D is at

Algebra ->  Coordinate-system -> SOLUTION: 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. Note: point A is at (0,4) and point D is at       Log On


   

Question 1131849: 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.
Note: point A is at (0,4) and point D is at (8,9)'
I got a hint from my teacher saying to reflect point A on the x axis. I don�t know what to do from there.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
points B(b,0) and C(c,10)
point A is at (0,4) and point D is at (8,9)
slope of AB is :
m=%284-0%29%2F%280-b%29=-4%2Fb
slope of BC is:
m=%2810-0%29%2F%28c-b%29=10%2F%28c-b%29
slope of CD is :
m=%289-10%29%2F%288-c%29=-1%2F%288-c%29
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:
-4%2Fb=-1%2F%288-c%29
4c-32=-b
4c=32-b............... (1)
The slope of BC is the opposite of the slope of AB:
10%2F%28c-b%29=4%2Fb
4c-4b=10b
4c=14b.............. (2)
from (1) and (2):
32-b=14b
32=14b%2Bb
15b=32
b=32%2F15
b=2%26+2%2F15

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solution and the answer in the post by @Mathlover1

https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1131849.html

is incorrect.


For the correct solution, see the post by tutor @greenestamps

https://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.1199273.html