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 the coordinates of M and J

Let the coordinate of $M = 2$ and the coordinate of $J=19$.

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

The formula to find the coordinate of 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, $m = 3$, $n = 1$, $x_1=2$ and $x_2 = 19$.
Substitute the values into the formula: $x=\frac{3\times19+1\times2}{3 + 1}$.

Step3: Calculate the numerator

$3\times19+1\times2=57 + 2=59$.

Step4: Calculate the denominator

$3 + 1=4$.

Step5: Find the coordinate of X

$x=\frac{59}{4}=14.75$.

Answer:

$14.75$