Question

refer to the number line. find the coordinate of point x such that the ratio of ax to xf is 1:3.
a -7
b -5
c -4
d 1
e 2
f 5

Explanation:

Step1: Identify coordinates of A and F

The coordinate of point A is - 7 and the coordinate of point F is 5.

Step2: Use the section - formula for one - dimensional case

If a point X divides the line - segment joining points \(x_1\) and \(x_2\) in the ratio \(m:n\), the coordinate of X is given by \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-7\), \(x_2 = 5\), \(m = 1\), and \(n = 3\).
\[x=\frac{1\times5+3\times(-7)}{1 + 3}\]

Step3: Simplify the expression

First, calculate the numerator: \(1\times5+3\times(-7)=5-21=-16\). Then, divide by the denominator: \(\frac{-16}{4}=-4\).

Answer:

• 4