Answer:
(-16/3,-17/3)
Explanation:
Let the point which is 2/3 of the way from C to D = X
It means that point X divides the line segment CD internally in the ratio 2:1.
To determine the coordinate of point X, we use the section formula for internal division of a line segment:
[tex](x,y)=\left\{ \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right\} [/tex][tex]\begin{gathered} (x_{1,}y_1)=(-3,-8) \\ (x_2,y_2)=(-6.5,-4.5) \\ m\colon n=2\colon1 \end{gathered}[/tex]
Substituting these values into the formula above, we have:
[tex]X(x,y)=\left\{ \frac{2(-6.5)+1(-3)}{2+1},\frac{2(-4.5)+1(-8)}{2+1}\right\} [/tex]
We then simplify:
[tex]\begin{gathered} X(x,y)=\left\{ \frac{-13-3}{3},\frac{-9-8}{3}\right\} \\ =\left\{ \frac{-16}{3},\frac{-17}{3}\right\} \end{gathered}[/tex]
Therefore, the exact coordinate of the point that is 2/3 of the way from C to D is (-16/3,-17/3).
