We have been given that point a is at [tex](-2,4)[/tex] and point c is at [tex](4,7)[/tex]. We are asked to find the coordinates of point b on segment ac such that the ratio is 1:3.
We will use section formula to solve our given problem.
When point P divides a segment internally in the ratio m:n, the coordinates of point P would be:
[tex][x=\frac{mx_2+nx_1}{m+n}, y=\frac{my_2+ny_1}{m+n}][/tex]
Let point [tex](-2,4)=(x_1,y_1)[/tex] and point [tex](4,7)=(x_2,y_2)[/tex].
[tex][x=\frac{1(4)+3(-2)}{1+3}, y=\frac{1(7)+3(4)}{1+3}][/tex]
[tex][x=\frac{4-6}{4}, y=\frac{7+12}{4}][/tex]
[tex][x=\frac{-2}{4}, y=\frac{19}{4}][/tex]
[tex][x=-0.5, y=4.75][/tex]
Therefore, the coordinates of point 'b' would be [tex](-0.5,4.75)[/tex].
