Question

1. if point s is between points r and t and s is the midpoint of rt, label the segment, find the value of x and the measures of st and rs. given: rt = 28 and st = 5x - 6. x =

st =
rs =

Explanation:

Step1: Use mid - point property

Since S is the mid - point of $\overline{RT}$, then $RS = ST$ and $RT=RS + ST = 2ST$. Given $RT = 28$, we have $2ST=28$, so $ST=\frac{RT}{2}=14$.

Step2: Solve for x

We know that $ST = 5x-6$ and $ST = 14$. So we set up the equation $5x-6 = 14$.
Add 6 to both sides: $5x=14 + 6=20$.
Divide both sides by 5: $x=\frac{20}{5}=4$.

Step3: Find RS

Since $RS = ST$ and $ST = 14$, then $RS = 14$.

Answer:

$x = 4$
$ST=14$
$RS = 14$