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=(1)/(2)BC`

Hence,

`(AB)/(BC)=(1)/(2)`

That is

`AB\colon BC=1\colon2`

The coordinates of B is given by

`\begin{gathered} B=((mx_2+nx_1)/(m+n),(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)`