Question

A segment with endpoints F (4, 9) and G (7, 2) is divided by a point H such that FH and GH form a 1:3 ratio. Find H. (5 points)
Select one:
a. (5.3, 6)
b. (4.75, 7.25)
c. (4.1, 7.4)
d. (5.25, 5.75)

Answer 1

@Yttrium @ganeshie8 @Nurali @lowcard2

Answer 2

@Yttrium @ganeshie8 @Nurali @lowcard2

Answer 3

If we look at the result objectively, we realize that the line must be divided into four parts. We then realize that the shorter segment must be FH. (Which will be one of the four units.)
To divide the line into four, we then use the midpoint formula. \[(\frac{ x+x \prime }{ 2 }, \frac{ y+y \prime }{ 2 })\]

Answer 4

Get the midpoint first. Can you @prowrestler ?

Answer 5

yes i can try

Answer 6

i got 5.5 for both

Answer 7

do it now

Answer 8

well, you're in good hands. I'll bow out.

Answer 9

let's name that point a A now. Get the mid point of A and F

Answer 10

i dont know that

Answer 11

you got (5.5,5.5) right? well check the mid point of (5.5,5.5) and (4,9)

Answer 12

how am i supposed to do that

Answer 13

same

Answer 14

what do you mean same

Answer 15

same method

Answer 16

i did and i got 5.5

Answer 17

Well, I was getting the length of FG. Then because the parts are in a ratio of 1:3, I was able to say how long FH needs to be.
That would allow us to sort through the points given to determine which one provides us the necessary length of FH.
It is working backwards, however, and so I was trying to sort through a way to work it out more directly.

Answer 18

What are you working on right now, topic-wise?
That might give me a clue as to the proper method...

Answer 19

I knew there had to be a more direct way to get the answer so I was working on it while we did these others.
So, let us say that we knew the value of x that point H must be at...
We can call that "x"

Answer 20

We know that the distance between the x-coordinate of F and H must be 1/3 of the distance between x and 7

Or you could write it differently, that 3 times the distance between F and H equals the distance between H and G.