The points given are (5, -6) and (4, 5).
Let the points be A and B.
The line segment is partitioned in the ratio 3 : 4, therefore we can call the point of the partition L.
[tex]\begin{gathered} (x_1,y_1)=(5,-6) \\ (x_2,y_2)=(4,5) \\ a\colon b=3\colon4 \\ \frac{b(x_1)+a(x_2)}{a+b},\frac{b(y_1)+a(y_2)}{a+b} \\ \text{Substitute for the values and you now have;} \\ L=\frac{4(5)+3(4)}{3+4},\frac{4(-6)+3(5)}{3+4} \\ L=\frac{20+12}{7},\frac{-24+15}{7} \\ L=\frac{32}{7},\frac{-9}{7} \end{gathered}[/tex]The coordinates (points) that partitions the given endpoints in the ratio 3:4 are
(32/7, -9/7)
