Given:
A has coordinates (-6,5)
C has coordinates (3.6,-0.4).
C divides AB in the ratio 3:2.
Refer to the diagram shown below.
The coordinates of B are determined by
![\frac{3.6-(-6)}{x-(-6)} = \frac{3}{3+2} \\ \frac{9.6}{x+6} = \frac{3}{5} \\ 3(x+6) = 48 \\ 3x +18=48 \\ x=30/3=10](https://tex.z-dn.net/?f=%20%5Cfrac%7B3.6-%28-6%29%7D%7Bx-%28-6%29%7D%20%3D%20%5Cfrac%7B3%7D%7B3%2B2%7D%20%5C%5C%20%5Cfrac%7B9.6%7D%7Bx%2B6%7D%20%3D%20%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%203%28x%2B6%29%20%3D%2048%20%5C%5C%203x%20%2B18%3D48%20%5C%5C%20x%3D30%2F3%3D10)
Also,
![\frac{5-(-0.4)}{5-y} = \frac{3}{5} \\ 3(5-y) = 27 \\ 15-3y=27 \\ y= \frac{12}{-3} =-4](https://tex.z-dn.net/?f=%20%5Cfrac%7B5-%28-0.4%29%7D%7B5-y%7D%20%3D%20%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%203%285-y%29%20%3D%2027%20%5C%5C%2015-3y%3D27%20%5C%5C%20y%3D%20%5Cfrac%7B12%7D%7B-3%7D%20%3D-4)
Answer:
The coordinates of B are (10,-4).
Now, we know the coordinates of line segment AB as A (-6, 5) and B (10,-4).
D (x,y) divides AB in the ratio 4:5.
Therefore
![\frac{x-(-6)}{10-(-6)} = \frac{4}{4+5} \\ \frac{x+6}{16} = \frac{4}{9} \\ 9(x+6)=64 \\ 9x+54=64 \\ x=1.11](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx-%28-6%29%7D%7B10-%28-6%29%7D%20%3D%20%5Cfrac%7B4%7D%7B4%2B5%7D%20%5C%5C%20%5Cfrac%7Bx%2B6%7D%7B16%7D%20%3D%20%5Cfrac%7B4%7D%7B9%7D%20%5C%5C%209%28x%2B6%29%3D64%20%5C%5C%209x%2B54%3D64%20%5C%5C%20x%3D1.11)
Also,
![\frac{5-y}{5-(-4)} = \frac{4}{9} \\ 5-y = 4 \\ y = 1](https://tex.z-dn.net/?f=%20%5Cfrac%7B5-y%7D%7B5-%28-4%29%7D%20%3D%20%5Cfrac%7B4%7D%7B9%7D%20%20%5C%5C%205-y%20%3D%204%20%5C%5C%20y%20%3D%201)
Answer:
The coordinates of D are (1.11, 1)