Question

if h is the midpoint of (overline{gi}), find gh. (gh = 5x + 2), (hi = 9x - 10) (diagram shows points g, h, i on a line with gh and hi labeled as above)

Explanation:

Step1: Set GH equal to HI (midpoint property)

Since \( H \) is the midpoint of \( \overline{GI} \), \( GH = HI \). So we set up the equation: \( 5x + 2 = 9x - 10 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides: \( 2 = 4x - 10 \)
Add 10 to both sides: \( 12 = 4x \)
Divide both sides by 4: \( x = 3 \)

Step3: Find \( GH \) by substituting \( x \)

Substitute \( x = 3 \) into \( GH = 5x + 2 \): \( GH = 5(3) + 2 = 15 + 2 = 17 \)

Answer:

\( 17 \)