Question

WILL GIVE MEDAL AND FAN

Answer 1

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.

Answer 2

Use the partition formula?

Answer 3

I dont think we've learned that yet.
This is advanced math homework our teacher gave us..

Answer 4

\[\large H=(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n})\]

Answer 5

im really confused as of right now...

Answer 6

this is supposed to be coordinate geometry, thats what he said..

Answer 7

@sourwing

Answer 8

@mathmale

Answer 9

@whpalmer4

Answer 10

@KittyKat77

Answer 11

@nm61101

Answer 12

@Hero

Answer 13

Use the formula.

Answer 14

i dont know what to substitute where...

Answer 15

we didnt actually learn this yet, could you help me with it??

Answer 16

m:n is ratio Here u have 5:1

x1.y1 and x2,y2 are the given 2 points.

Answer 17

ok i cant try but he said he wanted t=us to show our work and we're doing coordinate geometry so idk...

Answer 18

First, Chelsea, are you able to determine how much x changes as you go from Point B to Point Z?

Answer 19

And are you able to determine by how much y changes as you go from Point B to Point Z?

Answer 20

9, right?

Answer 21

I see that both x and y are increasing.

Answer 22

and for y it's 6..

Answer 23

Coordination geometry : http://en.wikipedia.org/wiki/Coordination_geometry
Partition(number theory) :
http://en.wikipedia.org/wiki/Partition_(number_theory)

Answer 24

That's right: 12 - 3 = 9.

Now please do the same thing to determine how much y changes.

Answer 25

to get from -1 to 5, you have to increase 6.

Answer 26

Perfect. Now, you want to go 1/5 th of the distance from B to Z, right? and to determine the point on the line connecting B to Z.

Answer 27

so we would multiply 9 by 1/5 and to the same to 6, right?

Answer 28

So, if the change in x is 9, and we want to go 1/5 of the way from B to Z, all we have to do is to multiply that 9 by (1/5). What do you get? Then, add your result to the x-coord. of b. That gives you the x coord of the point H.

Answer 29

Wow. You're ahead of me. Wonderful! So, now all u have to do is to determine the coordinates of point H.

Answer 30

and that would be 1 4/5 for the x coordinates and 1 1/5 for the y coordinates

Answer 31

Actually, that's the INCREASE in x from B(3,-1).

Answer 32

so i would add 1 4/5 to 9 and add 1 1/5 to 6?

Answer 33

but that doesnt seem to work??

Answer 34

@mathmale

Answer 35

@PsiSquared

Answer 36

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.

From B to Z along the x-axis, we go 12-3 = 9
From B to Z along the y-axis, we go 5-(-1) = 6

If we divide those distances into 5+1 = 6 parts (because we have a 5:1 partition), we'll take 5/6 of the distance and add it to B:

5/6*9 = 45/6 = 15/2
5/6*6 = 30/6 = 5
So we take point B(3,-1) and add 15/2 to the x coordinate and 6 to the y coordinate and get H(3+15/2,-1+5) = H(10.5,4)

Answer 37

Hello, Chelsea,

whpalmer's contribution has made it clear that I misread the original problem you posted. However, up to the part where you and I decided that x increased by 9 from (3,-1) to (12,5) and y by 6 from -1 to 5, we did just fine.

Point H is in between B and Z and divides up / partitions the line segment from B to Z in such a way that the initial part is 5/6 of the whole distance from B to Z, and the latter part is just 1/6 of that distance. That comes from the ratio 5:1. The initial part is 5 times as long as the latter part.

I'm going to use pretty much the same approach as has whpalmer.

We start at (3,-1) and add five sixths of the horizontal (x-)distance to 12,5) to it:
\[3+\frac{ 5 }{ 6 }(9)=3+\frac{ 45 }{ 6 }=3+\frac{ 15 }{ 2 }=\frac{ 6+15 }{ 2 }=10.5\] This is the x-coordinate of point H.

We start at (3,-1) and add five sixths of the vertical (y-distance) from (12,5) to it:\[-1+\frac{ 5 }{ 6 }6=-1+5 =4\] this is the y-coordinate of point H.

Therefore, point H is ( ? , ? )

Answer 38

YAY MEDAL FOR MATHMALE :D