Question

point s is on line segment rt. given rt = 4x, st = 5x - 10, and rs = 6, determine the numerical length of st.

Explanation:

Step1: Use segment - addition postulate

Since point S is on line segment RT, we have $RT=RS + ST$. Substituting the given expressions, we get $4x=6+(5x - 10)$.

Step2: Solve the equation for x

First, simplify the right - hand side of the equation: $4x=6 + 5x-10$, which simplifies to $4x=5x - 4$. Then, subtract $5x$ from both sides: $4x-5x=-4$, so $-x=-4$, and $x = 4$.

Step3: Find the length of ST

Substitute $x = 4$ into the expression for ST. We have $ST=5x-10$. Plugging in $x = 4$, we get $ST=5\times4-10$.

Step4: Calculate the value of ST

$ST=20 - 10=10$.

Answer:

10