Question

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.

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

i respectfully disagree with distance AB

Answer 5

What did you get?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

*don't

Answer 10

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

Answer 11

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

Answer 12

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