Question

I need to find a point that is a fraction of the distance between two other points, and I can't remember how to do it.

Answer 1

2 ducks and 3 pelicans

Answer 2

For sake of clarification I have to find a point that is 2/5 the distance between (6,2) and (8,4)

Answer 3

ok so let's take a peek a that

say we find the whole distance between those 2 points

and we divide it in say 5 pieces

so 2 pieces on one side.. and 3 pieces on the other side of that distance segment

what ratio would that make from the (6,2) to (8,4)?

Answer 4

What do you mean, what ratio can I get from that?

Answer 5

yes

Answer 6

How is yes an answer that question...?

Answer 7

notice we need to find the 2/5 distance
so we'd first split the distance in 5 pieces... and let us find the ratio of those 2 sides

Answer 8

well.. I meant yes, that's what we're looking for, the ratio.... what ratio would that make? :)

Answer 9

2 to 3?

Answer 10

I could've sworn there was just some formula for this... That's all I need.

Answer 11

yeap 2 to 3 or 2:3 FROM (6,2) to (8,4)

or so just gimme a few secs

Answer 12

\(\bf A(6,2)\qquad B(8,4)\qquad ratio1=2\qquad ratio2=3\qquad 2:3\\ \quad \\ \quad \\

\cfrac{AB}{BC}=\cfrac{ratio1}{ratio2}\implies ratio2\cdot AB=ratio1\cdot BC\quad \textit{dividing by B}\\ \quad \\
ratio2\cdot A=ratio1\cdot C\implies 3(6,2)=2(8,4)\\ \quad \\\qquad

{\color{blue}{ B=\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 \\
B=\left(\cfrac{(3\cdot 6)+(2\cdot 8)}{2+3}\quad ,\quad \cfrac{(3\cdot 2)+(2\cdot 4)}{2+3}\right)\)

Answer 13

Ok thanks

Answer 14

yw