Question

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.

Answer 1

@Directrix should i use the midpoint formula ??

Answer 2

i think you should use the internal division formula
take a look at this link this is good
http://www.teacherschoice.com.au/Maths_Library/Analytical%20Geometry/AnalGeom_3.htm

Answer 3

how to use it ??

Answer 4

The midpoint formula is not going to help here as best I see.

@luka1998 Did you calculate the length of segment ZB?

If so, what is it?

Answer 5

BY using Distance right ?

Answer 6

Yes.

Answer 7

@rajat97 Feel free to show us how to use this formula and apply it to this problem.

Answer 8

yup i'm on it @Directrix :)

Answer 9

let the point B(3,-1) be (x1,y1) and let the point Z (12,5) be (x2,y2) and let the segment be divided by the line in the ratio of 5:1 that is m:n by the point (x,y)
so by the internal division formula,
x=\[(n \times x1 + m \times x2)/m+n\]
and for the y-co-ordinate,
y=\[(n \times y1 + m \times y2)/m+n\]

Answer 10

@Directrix
d=squar root (x2-x1)^2+(y2-y1)^2
ZB=(12,5) (3,-1)
squar root (3-12)^2+(-1-5)^2
squar root 81+36 = squar root 117

Answer 11

i'll explain this in a better way but for this question , you can use what i have written
just wait for a minute

Answer 12

let q be the point that divides the line seg. PR in the ratio PQ:QR=m:n
so you should use the formula like this
m is the part of the ratio , farthest from the point R
so m goes in multiplication with the coordinates of point R for finding the co-ordinates
and the same goes with n and it goes in multiplication with the co-ordinates of P
if you don't understand this thing, just look at the formula that i have posted in my previous post and then read this once again carefully
this is ofcourse not the proof for this formula (lol) this is just for remembering purpose
hope this helps you !

Answer 13

@rajat97
is this correct
B(3,−1) Z(12,5) ratio of 5:1 at point P(x,y)
P(x,y)
( 5(3)+1(12)over 5+1, 5(−1)+1(5)over 5+1 )
(27 over 6, 0 over 6 )
(4.5 , 0)

Answer 14

nope!
you've done it reverse
i think it should be
B(3,−1) Z(12,5) ratio of 5:1 at point P(x,y)
P(x,y)
( 1(3)+5(12)over 5+1, 1(−1)+5(5)over 5+1 )
so this gives you
(63over6 , 24 over 6)
so p is (10.5 , 4)
hope this is correct!
well try!

Answer 15

and thanks for the medal

Answer 16

you are welcome and thx

Answer 17

it's my pleasure to help you

Answer 18

Thanks for the medals everybody!