Question

Find the coordinates of point G that lies along the directed line segment from F(-1, -1) to H(-8, 20) and partitions the segment in the ratio of 5:2.A. (-9, 19)B. (-5, 15)C. (-4.5, 9.5)D. (-6, 14)

Answer 1

It is given that the point G lies on the line segment FH and divides it in the ration 5:2.

So we will use the section formula to obtain the coordinates of the point G.

Now the x-coordinate of the point G will be:-

`\begin{gathered} G_x=(5(-8)+2(-1))/(5+2) \\ =(-40-2)/(7) \\ =(-42)/(7) \\ =-6 \end{gathered}`

Now the y-ccordinate of the point G will be:-

`\begin{gathered} G_y=(5(20)+2(-1))/(5+2) \\ =(100-2)/(7) \\ =(98)/(7) \\ =14 \end{gathered}`

So the coordinates of the point G are (-6, 14).

Hence the correct option is (D).