Question

The segment joining (1, -3) and (4, -6) is extended a distance equal to one sixth of its own length find the terminal point.

Answer 1

Answer:

Terminal point = (4.5 , -6.5)

Step-by-step explanation:

Let say Line segment Length = 6L

extended a distance equal to one sixth of its own length = 6L/6 = L

Total Length = 7L

Ratio of Line from initial Point & External Point = 7 : 1

Let say Terminal point (Tx , Ty)

Ratio : 7 : 1

Using Formula for externally dividing =  (mx₂ - nx₁)/(m-n) , (my₂ - ny₁)/(m-n)

m = 7 & n = 1   (x₁ , y₁) =(1 , -3)  &  (x₂ , y₂) =(4 , -6)  

Tx = (7(4) - 1(1) )/(7 -1)  = 27/6  = 4.5

Ty = (7(-6) - 1(-3)/(7 -1) = -39/6 = -6.5

Terminal point = (4.5 , -6.5)