Question

if h is the mid - point of $overline{gi}$, find $gh$.
$5x + 2$ $9x - 10$
$g$ $h$ $i$

Explanation:

Step1: Set up the equation

Since $H$ is the mid - point of $\overline{GI}$, then $GH = HI$. So, we set up the equation $5x + 2=9x - 10$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $5x+2 - 5x=9x - 10-5x$, which simplifies to $2 = 4x-10$. Then add 10 to both sides: $2 + 10=4x-10 + 10$, giving $12 = 4x$. Divide both sides by 4: $\frac{12}{4}=\frac{4x}{4}$, so $x = 3$.

Step3: Find $GH$

Substitute $x = 3$ into the expression for $GH$ which is $5x+2$. So, $GH=5\times3 + 2=15 + 2=17$.

Answer:

17