Question

Point A, located at (-8, 3), is the location of the storage closet and point C, located at (12, -4), is the director's office. Find point B, the location of the art supplies, if it is 2 over 5 the distance from point A to point C.

Answer 1

I DONT GET IT

Answer 2

so... where do you think we'd find our "art supplies" section?
we know is between point A and C

what's the distance between A and C anyway?

Answer 3

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
A&({\color{red}{ -8}}\quad ,&{\color{blue}{ 3}})\quad C&({\color{red}{ 12}}\quad ,&{\color{blue}{ -4}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

point B seems to be in between A and C, from A , B seems to be \(\bf \cfrac{2}{5}th\) from that distance

Answer 4

Thats where I get lost, Im not so sure how to find the distance between the two

Answer 5

Oh wait, yes I am sorry hold on

Answer 6

is it 21.2

Answer 7

hmmm

Answer 8

are you doing geometry?

Answer 9

yes

Answer 10

2/5 of 21.2 will be a distance
but rereading you.... seems it's asking for the actual x,y coordinates for point B

Answer 11

yeah it says the middle of A and C

Answer 12

well, it's not the middle, is 2/5 the way from A to C

Answer 13

so is a matter of 2 ratios

Answer 14

if I read you right

Answer 15

oh yeah okay sorry my brain is fried ive been spending 2 hours on this project... how do I know where 2/5 of the way is?

Answer 16

lemme show... you one... from 2 days... same thing, 2 ratios.... see if you can follow the example -> http://openstudy.com/study#/updates/52ec21c6e4b0a362a8947591

Answer 17

that one happens to use 1:3 ratios, yours is 2:5

Answer 18

I looked at it, still dont get it.

Answer 19

ok.... lemme rewrite it for this one

Answer 20

thanks

Answer 21

\(\bf \color{blue}{ A(-8,3)\qquad C(12,-4)\\ \quad \\ \quad \\

\cfrac{AB}{CB}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot AB=ratio1\cdot CB\quad \textit{dividing by B}\\ \quad \\
ratio2\cdot A=ratio1\cdot C}\implies 5(-8,3)=2(12,-4)\\ \quad \\\qquad B=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)\\ \quad \\

\qquad thus\qquad \\ \quad \\
B=\left(\cfrac{(5\cdot -8)+(2\cdot 12)}{2+5}\quad ,\quad \cfrac{(5\cdot 3)+(2\cdot -4)}{2+5}\right)\)

Answer 22

the asnwer is -0.9?

Answer 23

the answer would be an x,y coordinate set

Answer 24

oh no, uh I got -1.6 for this first and 7 for the second so im doing something wrong