Answer:
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
Step-by-step explanation:
When a point divides a line with coordinates (x1,y1) and (x2,y2) in ratio m:n,
the coordinates of point are given by:
[tex](x,y) = (\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n})[/tex]
Given points are:
(x1,y1) = (5,1)
(x2,y2) = (-5,4)
Putting the values in the formula
[tex]X(x,y) = (\frac{(1)(-5)+(4)(5)}{1+4} , \frac{(1)(4)+(4)(1)}{1+4})\\= (\frac{-5+20}{5}, \frac{4+4}{5})\\=(\frac{15}{5}, \frac{8}{5})\\=(3,\frac{8}{5})[/tex]
Hence,
The coordinates of point X that divides the line in 1:4 are: (3,8/5)
