Given A=(1,5), B=(x,2), and C=(4,-6) and the sum of AB+BC is to be a minimum, find the value of x.

Question

sooobored · Answer

distance formulaaaaaa
$$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$

calculusxy · Answer

I got the distance of AB to be $\sqrt{(x+1)^2 + 9}$

calculusxy · Answer

and the distance of BC is $\sqrt{(4-x)^2 + 64}$

sooobored · Answer

i respectfully disagree with distance AB

calculusxy · Answer

What did you get?

sooobored · Answer

x-1 and 2-(-5)=7

calculusxy · Answer

I am so sorry there was a typo. I just fixed it

calculusxy · Answer

The part of the problem that I do't understand is that their sum needs to be a minimum?

calculusxy · Answer

*don't

calculusxy · Answer

Sorry I have to go. Thanks for the help :)

sooobored · Answer

well, i assume the function d(x)=AB(x)+BC(x) will look something like a positive parabola
so you could use the first derivative

sooobored · Answer

and find where teh slope is equal to zero and thus the lowest point