Statement Problem: What are the coordinates of the point 3/4 of the way from A to B in the plotted graph?
Solution:
The coordinates of point A and B respectively is;
[tex]A(-5,-4),B(-3,3)[/tex]
The midpoint of the line segment AB is;
[tex]\begin{gathered} \text{Midpoint = (}\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ x_1=-5,y_1=-4,x_2=-3,y_2=3 \\ \text{Midpoint}=\text{ (}\frac{-5+(-3)}{2},\frac{-4+3}{2}) \\ \text{Midpoint}=(-\frac{8}{2},-\frac{1}{2}) \\ \text{Midpoint}=(-4,-0.5) \end{gathered}[/tex]
The coordinates of the point 3/4 of the way from A to B is the midpoint of the midpoint of line AB to B. That is;
[tex]\begin{gathered} M(-4,-0.5),B(-3,3) \\ \text{midpoint}=(\frac{-4+(-3)}{2},(\frac{-0.5+3}{2}) \\ \text{Midpoint}=(-\frac{7}{2},\frac{2.5}{2}) \\ \text{Midpoint}=(-3.5,1.25) \end{gathered}[/tex]
The required coordinates of the point 3/4 of the way from A to B is;
[tex](-3.5,1.25)[/tex]
