- anonymous

PLEASE HELP!!!! A point H on a segment with endpoints B(3, −1) and Z(12, 5) partitions the segment in a 5:1 ratio. Find H. You must show all work to receive credit.

- schrodinger

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- misty1212

HI!!

- misty1212

this looks hard, but i bet we can do it

- anonymous

i totally dont get it lol

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## More answers

- misty1212

yeah lets think for second and see what we can come up with

- imqwerty

u have a formula to find this :)

- misty1212

first off that means we are going to break it in to 6 equal parts, and take 5 of them

- misty1212

|dw:1440470612550:dw|

- imqwerty

the cordinates of point P(x,y) which lies on segment AB with end points A(a,b) and B(c,d) and divides it in the ration m:n
so u have -
x=(mc+na)/(m+n)
and
y=(md+nb)/(m+n)

- misty1212

yeah i don't get that formula
from 3 to 12 is 9 units
one sixth of that is \(\frac{9}{3}=\frac{3}{2}\)

- imqwerty

|dw:1440470712719:dw|

- anonymous

so is 3/2 the answer?

- misty1212

add \(5\times \frac{3}{2}\) to \(3\) and get \(10.5\)

- misty1212

no the answer is not a number, it is a point

- misty1212

the first coordinate of that point, if i am not mistaken, is \(10.5\)

- imqwerty

No the answer is (21/2, 3) :)

- misty1212

lol 21/2=10.5

- misty1212

now we need the second coordinate

- anonymous

so how did we get that again?

- misty1212

which, according to @imqwerty is 3

- imqwerty

@misty1212 u can go here to see the proof of formula - http://kea.kar.nic.in/vikasana/bridge/maths/chap_13.pdf :)

- misty1212

@imqwerty used a formula i don't know

- misty1212

you want to use the formula?

- anonymous

not really, i dont get it

- imqwerty

that^ link has the proof :)

- misty1212

so you want to do it without the formula?

- misty1212

your choice

- anonymous

nah

- misty1212

ok lets go slow then

- misty1212

first off, is it clear that if you want to break it in to a ratio that is 5:1 that is the same as dividing it up in to six parts, and taking five of them?

- anonymous

yea

- misty1212

ok so we are going to first break it in to six parts, then count out five
we have to do it twice, once for each coordinate

- misty1212

the first coordinate of one point is 3, of the other is 12
it is clear that they are 9 units apart?

- anonymous

yup

- misty1212

then we break that in to 6 pieces, so each will have length \(\frac{9}{6}\) or \(\frac{3}{2}\)

- misty1212

so far so good?

- anonymous

yes

- misty1212

ok now we want five of those, so staring at 3 we will add \(5\times \frac{3}{2}\) or if you prefer \(5\times 1.5\)

- misty1212

i get \[3+5\times 1.5=10.5\] as the first coordinate

- misty1212

now we can repeat with the second coordinates

- anonymous

okay

- misty1212

which is easier since they will be whole numbers

- misty1212

from -1 to 5 is 6 units right?

- misty1212

break that up in to 6 pieces each has length 1 since \(\frac{6}{6}=1\)

- misty1212

again we want to add five of those to \(-1\) so \(-1+5=4\)

- misty1212

answer:\[(10.5,4)\]

- misty1212

hmm not the same answer as @imqwerty got, but i am going to stick with that one

- anonymous

okay thanks for all your help

- misty1212

\[\color\magenta\heartsuit\]

- imqwerty

wait no

- misty1212

we can do it the formula way if you like see if we get the same answer

- imqwerty

24/6=4 sry for the mistake the answer is (10.5, 4)

- imqwerty

:)

- misty1212

i actually have never seen that formula thanks!

- imqwerty

welcome :)

- misty1212

\[\left(\frac{5\times 12+3}{6}, \frac{5\times 5-1}{6}\right)\]

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