Question

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

Explanation:

Step1: Determine the distance between A and F

The coordinate of A is - 7 and the coordinate of F is 5. The distance $AF=|5 - (-7)|=12$.

Step2: Use the ratio to find the distance of AX

Since the ratio of $AX$ to $XF$ is $1:3$, then the distance of $AX=\frac{1}{1 + 3}\times AF$. Substitute $AF = 12$ into the formula, we get $AX=\frac{1}{4}\times12 = 3$.

Step3: Calculate the coordinate of X

Let the coordinate of X be $x$. We know that $AX=x-(-7)$ (because A is at - 7). Since $AX = 3$, then $x+7=3$, so $x=3 - 7=-4$.

Answer:

-4