Question

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

Explanation:

Step1: Recall midpoint formula

The midpoint \( G \) of a segment with endpoints \( F \) (let its coordinate be \( x \)) and \( H \) (coordinate \( 4 \)) is given by the midpoint formula: \( \text{Midpoint} = \frac{x_F + x_H}{2} \). Here, the coordinate of \( G \) is \( -5 \), so we have \( -5=\frac{x + 4}{2} \).

Step2: Solve for \( x \)

Multiply both sides of the equation \( -5=\frac{x + 4}{2} \) by \( 2 \): \( -5\times2=x + 4 \), which simplifies to \( -10=x + 4 \). Then subtract \( 4 \) from both sides: \( x=-10 - 4=-14 \).

Answer:

The location of \( F \) is \(-14\).