Solution:
As we know that if a point P divides the line AB in the ratio m:n. Then the coordinates of the point P is given by the formula
[tex]P=(\frac{mx_1+nx_2}{m+n} ,\frac{my_1+ny_2}{m+n})\\
\\
\text{where (x 1,y1)and (x2,y2) represents the coordinates of the end points.}[/tex]
Here [tex]m:n=2:4, A=(-2,6), B=(4,-6)[/tex]
[tex]P=(\frac{2*(-2)+4*4}{2+4} ,\frac{2*6+4*(-6)}{2+4}) [/tex]
[tex]P=(\frac{12}{6} ,\frac{-12}{6}) [/tex]
[tex]P=(2 ,-2) [/tex]
Hence the required coordinate is (2,-2)
