Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.

Respuesta :

(8,5)

To find the point of the ratio 1:4 going from (10,4) you need to find the midpoint of (10,4) and (2,8). the midpoint formula is:
[tex] (\frac{ x_{1} + x_{2} }{2}, \frac{ y_{1} + y_{2} }{2})[/tex]
Plug in values to solve
[tex](\frac{10 + 2 }{2}, \frac{ 4 + 8}{2}) = (6,6)[/tex]
then find the midpoint of (10,4) and (6,6)
[tex](\frac{10 + 6 }{2}, \frac{ 4 + 6}{2}) = (8,5)[/tex]