anonymous
  • 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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
this looks hard, but i bet we can do it
anonymous
  • anonymous
i totally dont get it lol

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More answers

misty1212
  • misty1212
yeah lets think for second and see what we can come up with
imqwerty
  • imqwerty
u have a formula to find this :)
misty1212
  • misty1212
first off that means we are going to break it in to 6 equal parts, and take 5 of them
misty1212
  • misty1212
|dw:1440470612550:dw|
imqwerty
  • 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
  • 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
  • imqwerty
|dw:1440470712719:dw|
anonymous
  • anonymous
so is 3/2 the answer?
misty1212
  • misty1212
add \(5\times \frac{3}{2}\) to \(3\) and get \(10.5\)
misty1212
  • misty1212
no the answer is not a number, it is a point
misty1212
  • misty1212
the first coordinate of that point, if i am not mistaken, is \(10.5\)
imqwerty
  • imqwerty
No the answer is (21/2, 3) :)
misty1212
  • misty1212
lol 21/2=10.5
misty1212
  • misty1212
now we need the second coordinate
anonymous
  • anonymous
so how did we get that again?
misty1212
  • misty1212
which, according to @imqwerty is 3
imqwerty
  • imqwerty
@misty1212 u can go here to see the proof of formula - http://kea.kar.nic.in/vikasana/bridge/maths/chap_13.pdf :)
misty1212
  • misty1212
@imqwerty used a formula i don't know
misty1212
  • misty1212
you want to use the formula?
anonymous
  • anonymous
not really, i dont get it
imqwerty
  • imqwerty
that^ link has the proof :)
misty1212
  • misty1212
so you want to do it without the formula?
misty1212
  • misty1212
your choice
anonymous
  • anonymous
nah
misty1212
  • misty1212
ok lets go slow then
misty1212
  • 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
  • anonymous
yea
misty1212
  • 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
  • misty1212
the first coordinate of one point is 3, of the other is 12 it is clear that they are 9 units apart?
anonymous
  • anonymous
yup
misty1212
  • misty1212
then we break that in to 6 pieces, so each will have length \(\frac{9}{6}\) or \(\frac{3}{2}\)
misty1212
  • misty1212
so far so good?
anonymous
  • anonymous
yes
misty1212
  • 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
  • misty1212
i get \[3+5\times 1.5=10.5\] as the first coordinate
misty1212
  • misty1212
now we can repeat with the second coordinates
anonymous
  • anonymous
okay
misty1212
  • misty1212
which is easier since they will be whole numbers
misty1212
  • misty1212
from -1 to 5 is 6 units right?
misty1212
  • misty1212
break that up in to 6 pieces each has length 1 since \(\frac{6}{6}=1\)
misty1212
  • misty1212
again we want to add five of those to \(-1\) so \(-1+5=4\)
misty1212
  • misty1212
answer:\[(10.5,4)\]
misty1212
  • misty1212
hmm not the same answer as @imqwerty got, but i am going to stick with that one
anonymous
  • anonymous
okay thanks for all your help
misty1212
  • misty1212
\[\color\magenta\heartsuit\]
imqwerty
  • imqwerty
wait no
misty1212
  • misty1212
we can do it the formula way if you like see if we get the same answer
imqwerty
  • imqwerty
24/6=4 sry for the mistake the answer is (10.5, 4)
imqwerty
  • imqwerty
:)
misty1212
  • misty1212
i actually have never seen that formula thanks!
imqwerty
  • imqwerty
welcome :)
misty1212
  • misty1212
\[\left(\frac{5\times 12+3}{6}, \frac{5\times 5-1}{6}\right)\]

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