Question

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

Explanation:

Step1: Identify the coordinates of S and U

The coordinate of S is 5 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 M 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, \(x_1 = 5\), \(x_2=9\), \(m = 2\), and \(n = 3\).
\[x=\frac{2\times9+3\times5}{2 + 3}\]

Step3: Calculate the numerator

\[2\times9+3\times5=18 + 15=33\]

Step4: Calculate the denominator

\[2+3 = 5\]

Step5: Find the value of x

\[x=\frac{33}{5}=6.6\]

Answer:

6.6