Question

the point g is the midpoint of $overline{fh}$. find the location of f.

Explanation:

Step1: Recall mid - point formula

If $G$ is the mid - point of $\overline{FH}$, and the coordinates of $F$ is $x_F$, $G$ is $x_G$ and $H$ is $x_H$, then $x_G=\frac{x_F + x_H}{2}$.

Step2: Rearrange the formula to solve for $x_F$

We can rewrite the formula as $2x_G=x_F + x_H$, and then $x_F=2x_G−x_H$.

Step3: Substitute the given values

Given $x_G = 8$ and $x_H=21$, we substitute them into the formula: $x_F=2\times8 - 21$.

Step4: Calculate the value of $x_F$

$x_F = 16-21=- 5$.

Answer:

$-5$