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 the y value for H.

a)6.75
b)7.25
c)8.25
d)5.75

Answer 1

help pleeeease

Answer 2

@jdoe0001 hey can you please try this one? :)

Answer 3

so the line looks like

Answer 4

so.. gimme one sec

Answer 5

ok

Answer 6

\(\bf F(4,9)\qquad G(7,2)\qquad ratio1=1\qquad ratio2=3\qquad 1:3\\ \quad \\ \quad \\

\cfrac{FH}{GH}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot FH=ratio1\cdot GH\quad \textit{dividing by H}\\ \quad \\
ratio2\cdot F=ratio1\cdot G\implies 3(4,9)=1(7,2)\\ \quad \\\qquad

{\color{blue}{ H=\left(\cfrac{\textit{sum of "x" values}}{ratio1+ratio2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{ratio1+ratio2}\right)}}\\ \quad \\

\qquad thus\qquad \\ \quad \\
H=\left(\cfrac{(3\cdot 4)+(1\cdot 7)}{1+3}\quad ,\quad \cfrac{(3\cdot 9)+(1\cdot 2)}{1+3}\right)\)

Answer 7

ok i got (4.75, 7.5) now what do i do with that?

Answer 8

@jdoe0001

Answer 9

so yes.. .that's correct.. so recall find the \({\color{brown}{ y\ value}}\) for H.

Answer 10

so which of the answer choices?

Answer 11

well what's the y-coordinate for H that you found?

Answer 12

7.5... but the answer choice has 7.25

Answer 13

hmmm ohh I see. . misread you a bit

right... recheck your calculation for "y" :)

Answer 14

\(\bf \cfrac{(3\cdot 9)+(1\cdot 2)}{1+3}\)

Answer 15

yes lol i always mistype something on my calculator lol thanks for the help

Answer 16

yw

Answer 17

sooo the answer is 7.25?