The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. What are the coordinates of the point P on the line segment such that P is the length of the line segment from G?

The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. Hence the required coordinate point is (9/4, 11/4).

What is the coordinate of the point which divides a line segment in a specified ratio?

Suppose that there is a line segment [tex]\overline{AB}[/tex] such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

where we have:

the coordinate of A is[tex](x_1, y_1)[/tex]

and the coordinate of B is [tex](x_2, y_2)[/tex]

The coordinate point between two points P and G divided between ratios a and b is expressed as;

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]

Given the coordinate points F(3, 5) and G(0, –4) divided within the ratio 1:3

[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{1(0) + 3(3)}{1+3} , \dfrac{1(-4)+ 3(5)}{1+3} \right)\\\\(x,y) = \left( \dfrac{9}{4} , \dfrac{11}{4} \right)[/tex]

Hence the required coordinate point is (9/4, 11/4).

Learn more about a point dividing a line segment in a ratio here:

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