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A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G. What are the coordinates of G?

Sagot :

Given:

A directed line segment begins at F(-8, -2), ends at H(8, 6), and is divided in the ratio 8 to 2 by G.

To find:

The coordinates of point G.

Solution:

Section formula: If a point divide a line segment with end points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in m:n, then the coordinates of that point are

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

Point G divide the line segment FH in 8:2. Using section formula, we get

[tex]G=\left(\dfrac{8(8)+2(-8)}{8+2},\dfrac{8(6)+2(-2)}{8+2}\right)[/tex]

[tex]G=\left(\dfrac{64-16}{10},\dfrac{48-4}{10}\right)[/tex]

[tex]G=\left(\dfrac{48}{10},\dfrac{44}{10}\right)[/tex]

[tex]G=\left(4.8,4.4\right)[/tex]

Therefore, the coordinates of point G are (4.8, 4.4).

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