Question

which of the following are the coordinates of point B on the directed line segment AC, such that AB is 1/5 of AC?

Answer 1

The coordinates of point B is;

`(5,-7)`

Step-by-step explanation:

Given the attached image;

The coordinate of point A is;

`(8,-8)`

The coordinate of point C is;

`(-7,-3)`

If AB is 1/5 of AC;

`\Delta x_(AB)=(1)/(5)(\Delta x_(AC))_{}_{}_{}_{}_{}_{}`

So; let (x,y) represent the coordinates of B;

`\begin{gathered} (8-x)=(1)/(5)(8-(-7)) \\ 8-x=(1)/(5)(15) \\ 8-x=3 \\ x=8-3 \\ x=5 \end{gathered}`

The same applies to y coordinate;

`\Delta y_(AB)=(1)/(5)(\Delta y_(AC))_{}`

So;

`\begin{gathered} (-8-y)=(1)/(5)(-8-(-3)) \\ -8-y=(1)/(5)(-8+3) \\ -8-y=(1)/(5)(-5) \\ -8-y=-1 \\ y=-8+1 \\ y=-7 \end{gathered}`

Therefore, the coordinates of point B is;

`(5,-7)`