Answer:
The coordinates of point B is;
[tex](5,-7)[/tex]
Explanation:
Given the attached image;
The coordinate of point A is;
[tex](8,-8)[/tex]
The coordinate of point C is;
[tex](-7,-3)[/tex]
If AB is 1/5 of AC;
[tex]\Delta x_{AB}=\frac{1}{5}(\Delta x_{AC})_{}_{}_{}_{}_{}_{}[/tex]
So; let (x,y) represent the coordinates of B;
[tex]\begin{gathered} (8-x)=\frac{1}{5}(8-(-7)) \\ 8-x=\frac{1}{5}(15) \\ 8-x=3 \\ x=8-3 \\ x=5 \end{gathered}[/tex]
The same applies to y coordinate;
[tex]\Delta y_{AB}=\frac{1}{5}(\Delta y_{AC})_{}[/tex]
So;
[tex]\begin{gathered} (-8-y)=\frac{1}{5}(-8-(-3)) \\ -8-y=\frac{1}{5}(-8+3) \\ -8-y=\frac{1}{5}(-5) \\ -8-y=-1 \\ y=-8+1 \\ y=-7 \end{gathered}[/tex]
Therefore, the coordinates of point B is;
[tex](5,-7)[/tex]
