Question

refer to the number line. find the coordinate of point x such that the ratio of bx to xf is 3:2.

Explanation:

Step1: Identify the coordinates of B and F

The coordinate of B is - 5 and the coordinate of F is 5.

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 two points \(x_1\) and \(x_2\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-5\) (coordinate of B), \(x_2 = 5\) (coordinate of F), \(m = 3\), and \(n = 2\).
\[x=\frac{3\times5+2\times(-5)}{3 + 2}\]

Step3: Simplify the expression

First, calculate the numerator: \(3\times5+2\times(-5)=15-10 = 5\). Then, the denominator is \(3 + 2=5\). So, \(x=\frac{5}{5}=1\).

Answer:

1