Question

use the image to answer the question.

determine the coordinates of point g, that divides the line ab into two segments with lengths in a ratio of 3:5.
(1 point)
g is located at (□,□)
check answer remaining attempts 3

Explanation:

Step1: Find the length of AB

From the graph, \(A=(0,0)\) and \(B=(8,0)\). The length of \(AB\) is \(8 - 0=8\) units.

Step2: Use the section formula for one - dimensional case

If a point \(G\) divides the line segment from \(A(x_1)\) to \(B(x_2)\) in the ratio \(m:n\), the formula for the coordinate of \(G\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(m = 3\), \(n = 5\), \(x_1=0\), \(x_2 = 8\).
Substitute the values into the formula: \(x=\frac{3\times8+5\times0}{3 + 5}=\frac{24}{8}=3\)

Answer:

\((3,0)\)