Question

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are

Answer 1

I just had to do this problem and,

B is (10, -4) and D is (58/9, -2)

Explanation:

Answer 2

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

`(3.6-(-6))/(x-(-6)) = (3)/(3+2) \\ (9.6)/(x+6) = (3)/(5) \\ 3(x+6) = 48 \\ 3x +18=48 \\ x=30/3=10`
Also,

`(5-(-0.4))/(5-y) = (3)/(5) \\ 3(5-y) = 27 \\ 15-3y=27 \\ y= (12)/(-3) =-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

`(x-(-6))/(10-(-6)) = (4)/(4+5) \\ (x+6)/(16) = (4)/(9) \\ 9(x+6)=64 \\ 9x+54=64 \\ x=1.11`
Also,

`(5-y)/(5-(-4)) = (4)/(9) \\ 5-y = 4 \\ y = 1`

Answer:
The coordinates of D are (1.11, 1)