Question

What are the coordinates of point B on AC such that AB BC'? y 7 5 2 1+ + 1 ) > I 1 2 3 4 5 6 7 -7-6-5-4-3-2 -2- -37 -4+ -5 +

Answer 1

The point at A has coordinates (6, -7)

The point at C has coordinates (-3, -2)

$AB=\frac{1}{2}BC$

Hence,

$\frac{AB}{BC}=\frac{1}{2}$

That is

$AB\colon BC=1\colon2$

The coordinates of B is given by

$\begin{gathered} B=(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}) \\ \text{Where} \\ AB\colon BC=m\colon n \end{gathered}$

In this case,

m:n=1:2,

therefore, we can have

m=1, n=2.

Also

$(x_1,y_1)=(6,-7)$