Question

A (0,0)
B (8,0)

Determine the coordinate of point G, that divides the line AB into two segments with lengths in a ration of 3:5.

G is located at (_,_)

Answer 1

To find the coordinates of point G that divides segment AB in a ratio of 3:5, we can use the section formula. The coordinates of A are (0, 0) and the coordinates of B are (8, 0).

Let the ratio of the segments be \( m:n = 3:5 \). Here, \( m = 3 \) and \( n = 5 \).

The formula to find the coordinates \( (x, y) \) of the point G that divides the line segment joining two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in the ratio \( m:n \) is given by:

\[
x = \frac{mx_2 + nx_1}{m+n}
\]
\[
y = \frac{my_2 + ny_1}{m+n}
\]

Substituting the values:

- \( x_1 = 0, y_1 = 0 \) (for point A)
- \( x_2 = 8, y_2 = 0 \) (for point B)
- \( m = 3, n = 5 \)

Now, let's calculate the x-coordinate of G:

\[
x = \frac{3 \cdot 8 + 5 \cdot 0}{3 + 5} = \frac{24 + 0}{8} = \frac{24}{8} = 3
\]

Now, let's calculate the y-coordinate of G:

\[
y = \frac{3 \cdot 0 + 5 \cdot 0}{3 + 5} = \frac{0 + 0}{8} = \frac{0}{8} = 0
\]

Thus the coordinates of point G are:

\[
G (3, 0)
\]

So, G is located at \( (3, 0) \).