Question

refer to the number line. find the coordinate of point x such that the ratio of mx to xj is 3:1.

Explanation:

Step1: Identify coordinates of M

The coordinate of point M is 3.

Step2: Let the coordinate of X be \(x\)

We know that the ratio \(MX:XJ = 3:1\). Let the coordinate of \(J = 18\). The distance between \(M\) and \(J\) is \(18 - 3=15\).

Step3: Use the ratio - division formula

Since \(MX:XJ=3:1\), the point \(X\) divides the line - segment \(MJ\) in the ratio \(3:1\). The formula for a point \(X\) that divides the line - segment joining \(M(x_1)\) and \(J(x_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(m = 3\), \(n = 1\), \(x_1=3\), and \(x_2 = 18\).
\[x=\frac{3\times18+1\times3}{3 + 1}=\frac{54 + 3}{4}=\frac{57}{4}=14.25\]

Answer:

14.25