Question

question point s is on line segment rt. given rt = 3x, rs = 3x - 5, and st = 3x - 1, determine the numerical length of rt. answer attempt 1 out of 2 rt =

Explanation:

Step1: Use segment - addition postulate

Since $RT=RS + ST$, we substitute the given expressions: $3x=(3x - 5)+(3x - 1)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(3x - 5)+(3x - 1)=3x-5 + 3x-1=6x-6$. So, the equation becomes $3x=6x - 6$.

Step3: Solve for $x$

Subtract $3x$ from both sides: $0 = 6x-3x - 6$, which simplifies to $0 = 3x-6$. Then add 6 to both sides: $3x=6$, and divide by 3 to get $x = 2$.

Step4: Find the length of $RT$

Substitute $x = 2$ into the expression for $RT$. Since $RT = 3x$, then $RT=3\times2=6$.

Answer:

6