contestada

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)

Respuesta :

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:-

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

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

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

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

Hence the correct option is (D).

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