Hello, strwbrry869!

Determine the shortest distance from point to the x-axis to point There is a back-door approach to this problem. Code:

| _
| (4,√7)
| o B'
| * :
-5 | P * :
---+--------------+--o--------+----
: * * :
: * | * :
: * | o B_
: * | (4,-√7)
: * |
A o _ |
(-5,-2√7) |

Reflect point over the -axis to point

Draw line , intersecting the -axis at

gives the shortest distance from to plus from to

. . (Do you see why?)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Using calculus, the problem gets VERY messy!

The distance from to is:

.

The distance from to is:

. .

The total distance is: .

And *that* is the function we must minimize . . .