Question

A(2,-2) B(11,-4) find AC + BC is a bare minimum on X axis... Show ur work too mates

Answer 1

can't wait to see the answer to this...

Answer 2

more information?
what course is this from?

Answer 3

as it is now, I don't think there is an answer, and that's what sate is most likely saying to us-:(

Answer 4

or wait...

Answer 5

okay, say you have a function
\(\large\color{black}{ y={\rm AC} +{\rm BC}}\)
\(\large\color{black}{ y={\rm C(A} +{\rm B)}}\)
I will assume to exclude any values of C equal to or less than 0.

I get that for \(\large\color{black}{ y\rightarrow0}\), \(\large\color{black}{ C\rightarrow0}\).

this is the best I can get. (assuming that A and B are positive)

Answer 6

with more info, we could do more

Answer 7

that is all the info ive obtained

Answer 8

oh and the course is Geometry

Answer 9

honors Geometry

Answer 10

@SolomonZelman

Answer 11

check out this page

http://hom.wikidot.com/heron

Answer 12

Thx Jem @jim_thompson5910

Answer 13

\(\huge\cal\color{indigo}{Welcome~to~Openstudy!~:)}\) @Da_Homie

Answer 14

oh, tnx for editing it.

Answer 15

\(\large\color{black}{ A(2,-2)~~~B(11,-4) }\)
and you may be mean,

` find C so that AC + BC is a bare minimum on X axis` ?

Answer 16

yea

Answer 17

oh, that is much better.
I am not very sure what a bear minimum on x-axis means.

Answer 18

lol what is the minimum distance it can be

Answer 19

minimum distance Ac + BC is

Answer 20

for it to be on the x-axis. right?

Answer 21

for it, for C to be on x-axis.

\(\large\color{black}{ A(2,-2)~~~B(11,-4) }\)
https://www.desmos.com/calculator/wyfre5igq8

showing the pic of the 2 points.

Answer 22

yes exactly my friend

Answer 23

it would be logical to say that the closer 2 sides to each other are, the more likely will it be a minimum:
(As, \(\large\color{black}{ 4^2+4^2<8^2+2^2 }\) . not exactly like this, but idea is same)

\(\large\color{black}{ AB=\sqrt{9^2+4^2}=\sqrt{81+16}=\sqrt{95} }\) (just in case we need it)

Answer 24

it would be logical to say that the closer 2 sides to each other are, the more likely will it be a minimum:
(As, \(\large\color{black}{ 4^2+4^2<8^2+2^2 }\) . not exactly like this, but idea is same)

\(\large\color{black}{ AB=\sqrt{9^2+4^2}=\sqrt{81+16}=\sqrt{95} }\) (just in case we need it)

Answer 25

when \(\large\color{black}{ AC=BC }\) would get a minimum distance:
Solving for C.

\(\large\color{black}{ \sqrt{(2-x_c)^2+(-2-y_c)^2}=\sqrt{(11-x_c)^2+(-4-y_c)^2} }\)

Answer 26

where point C is \(\large\color{black}{ (x_c,y_c) }\)

Answer 27

thats the equation???

Answer 28

I will use just x and y, without sub c.

Answer 29

got disconnected, dang it

Answer 30

I am raising both sides to second power, and plugging in y=0, since that is what I want to find (at the y axis)

Answer 31

ok, im with u

Answer 32

\(\large\color{black}{ (2-x)^2+4=(11-x)^2+16 }\)

Answer 33

\(\large\color{black}{ 4-4x+x^2+4=121-22x+x^2+16 }\)

Answer 34

\(\large\color{black}{ 4x+x^2+4=117-22x+x^2+16 }\)

\(\large\color{black}{ 4-4x+4=121-22x+16 }\)

\(\large\color{black}{ -4x+8=137-22x }\)

\(\large\color{black}{ 16x=129 }\)

\(\large\color{black}{ x=129/16 }\)

Answer 35

i got 8.0825 :(
i think its wrong

Answer 36

So I am thinking it would be \(\large\color{black}{ C~~(129,16~,0) }\)

Answer 37

when I graph the points I get:
https://www.desmos.com/calculator/ujh6gbdujs

Answer 38

what did you get for X??

Answer 39

the x coordinate of the point I got is 129/16

Answer 40

but that would be a decimal right?

Answer 41

8.0825

Answer 42

8.0625 is what I get

Answer 43

8.0625*

Answer 44

i meant 6
lol

Answer 45

I am not 100% sure about my solution though.

Answer 46

same

Answer 47

looks like I got it write, like after graphing, doesn't seem to have some crazy non sense

Answer 48

how did u graph that anyway??

Answer 49

I polted in a graphing calculator

Answer 50

@plotted

Answer 51

ohh nvm i was thinkng something else lol

Answer 52

Step 1) Plot the two points A and B

Step 2) Pick a point you want to reflect over the x axis, say B. When you reflect B over, it will land on B'

Step 3) Construct the line AB'

Step 4) The point of intersection between AB' and the x axis is where C should go to minimize AC+BC.

This is shown in the link

http://hom.wikidot.com/heron