Question

If the segment AB, where A(-3, 1) and B(2, 5), is extended beyond B to a point P twice as far from A as B is, find P. Can you please help me it's for my friend thank you :)

Answer 1

There is a section fomrula to it it
If a point \((a,b)\) divides a segment with vertices \((x_1,y_1)\) and \((x_2,y_2)\) in ratio \((m:n)\)

then the point is given by \(a=\dfrac{mx_2+nx_1}{m+n}\)
and
\(b=\dfrac{my_2+ny_1}{m+n}\)

Answer 2

@JianEnriquez here you go :)

Answer 3

here \((a,b)=(2,5)\)

\(m:n::1:2\)

\((x_1,y_1)=(-3,1)\)
and
\((x_2,y_2)=(x,y)\)

Answer 4

Thank you :D, i never knew about that formula though, but @mathmath333 is it possible to get the point using distance formula aswell?

Answer 5

yes it would be possible but the section formula is easy that i have shown.

Answer 6

Thank you @mathmath333 :D

Answer 7

WELCOME TO OPENSTUDY !!! @JianEnriquez WOOHOOO :D

Answer 8

Alright, thanks @mathmath333 and thank you @martaamador62 :D

Answer 9

\[ \Huge \begin{array}l\color{red}{\text{W}}\color{orange}{\text{e}}\color{#E6E600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{t}}\color{#E6E600}{\text{o}}\color{green}{\text{ }}\color{blue}{\text{O}}\color{purple}{\text{p}}\color{purple}{\text{e}}\color{red}{\text{n}}\color{orange}{\text{s}}\color{#E6E600}{\text{t}}\color{green}{\text{u}}\color{blue}{\text{d}}\color{purple}{\text{y}}\color{purple}{\text{.}}\color{red}{\text{c}}\color{orange}{\text{o}}\color{#E6E600}{\text{m}}\color{green}{\text{ }}\color{blue}{\text{.}}\color{purple}{\text{}}\end{array} \]