Question

Given AB with A <2, 7,-5> and B <-3,-8, 0>, find the coordinates of C if C divides AB one fifth of the way from A to B.

Answer 1

(1,4,-4).

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

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n),(mz_2+nz_1)/(m+n)\right)`

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

`C=\left((1(-3)+4(2))/(1+4),(1(-8)+4(7))/(1+4),(1(0)+4(-5))/(1+4)\right)`

`C=\left((-3+8)/(5),(-8+28)/(5),(0-20)/(5)\right)`

`C=\left((5)/(5),(20)/(5),(-20)/(5)\right)`

`C=\left(1,4,-4\right)`

Therefore, the coordinates of C are (1,4,-4).