Answer :
Answer:
(1,4,-4).
Step-by-step explanation:
Note: Consider A(2, 7,-5) and B (-3,-8, 0).
Section formula: If a point divides a line segment in m:n, then coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n},\dfrac{mz_2+nz_1}{m+n}\right)[/tex]
It is given that C divides AB one fifth of the way from A to B. It means AC:AB=1:5
AC:CB=1:(5-1)=1:4
Using the above formula, we get
[tex]C=\left(\dfrac{1(-3)+4(2)}{1+4},\dfrac{1(-8)+4(7)}{1+4},\dfrac{1(0)+4(-5)}{1+4}\right)[/tex]
[tex]C=\left(\dfrac{-3+8}{5},\dfrac{-8+28}{5},\dfrac{0-20}{5}\right)[/tex]
[tex]C=\left(\dfrac{5}{5},\dfrac{20}{5},\dfrac{-20}{5}\right)[/tex]
[tex]C=\left(1,4,-4\right)[/tex]
Therefore, the coordinates of C are (1,4,-4).