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

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

$Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n},\dfrac{mz_2+nz_1}{m+n}\right)$

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

$C=\left(\dfrac{1(-3)+4(2)}{1+4},\dfrac{1(-8)+4(7)}{1+4},\dfrac{1(0)+4(-5)}{1+4}\right)$

$C=\left(\dfrac{-3+8}{5},\dfrac{-8+28}{5},\dfrac{0-20}{5}\right)$

$C=\left(\dfrac{5}{5},\dfrac{20}{5},\dfrac{-20}{5}\right)$

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

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