Question

Find the coordinates of the point P which is five-sixth of the way from A(2, 3, –4) to B(8, –3, 2).

Answer 1

The coordinates are (7, −2 , 1).

Step-by-step explanation:

Given:

Let P (x,y,z) be the required point

P divides AB in the ratio 5 : 1.

So,

P (x, y, z) = $(\frac{5(8)+1(2)}{5+1} ,\frac{5(-3)+1(3)}{5+1} ,\frac{5(2)+1(-4)}{5+1} )$

               = $(\frac{40+2}{6} ,\frac{-15+3}{6} ,\frac{10-4}{6} )$                

               = $(\frac{42}{6} ,\frac{-12}{6} ,\frac{6}{6} ,)$

               = (7, −2 , 1)

Therefore P (7, −2 , 1) are the coordinates of the point P.