Question

refer to the number line. find the coordinate of point x such that the ratio of mx to xj is 3:1. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 m j

Explanation:

Step1: Identify coordinates of M and J

The coordinate of M is 2 and the coordinate of J is 18.

Step2: Use section - formula for one - dimensional case

If a point X divides the line - segment joining M(x1) and J(x2) in the ratio m:n, the coordinate of X is given by \(x=\frac{mx_2+nx_1}{m + n}\). Here, m = 3 and n = 1, x1 = 2, x2 = 18.
\[x=\frac{3\times18+1\times2}{3 + 1}\]

Step3: Calculate the value of x

First, calculate the numerator: \(3\times18+1\times2=54 + 2=56\). Then, divide by the denominator: \(\frac{56}{4}=14\).

Answer:

14