Question

find the coordinate of point g such that the ratio of rg to gu is 3:2.
p q r s t u
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
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Explanation:

Step1: Identify the coordinates of R and U

The coordinate of R is - 1 and the coordinate of U is 9.

Step2: Use the section - formula for a one - dimensional line

The formula to find the coordinate of a point G that divides the line segment joining points \(x_1\) and \(x_2\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-1\), \(x_2 = 9\), \(m = 3\), and \(n = 2\).
\[x=\frac{3\times9+2\times(-1)}{3 + 2}\]

Step3: Calculate the numerator

\[3\times9+2\times(-1)=27-2=25\]

Step4: Calculate the denominator

\[3 + 2=5\]

Step5: Find the coordinate of G

\[x=\frac{25}{5}=5\]

Answer:

5