Question

question point s is on line segment rt. given rt = x + 5, st = 4x - 9, and rs = x - 2, determine the numerical length of rt. answer attempt 1 out of 1 rt =

Explanation:

Step1: Use segment - addition postulate

Since point S is on line segment RT, we have $RS + ST=RT$. Substituting the given expressions: $(x - 2)+(4x - 9)=x + 5$.

Step2: Simplify the left - hand side

Combine like terms: $x-2 + 4x-9=5x-11$. So, $5x-11=x + 5$.

Step3: Solve for x

Subtract x from both sides: $5x-x-11=x - x+5$, which gives $4x-11 = 5$. Then add 11 to both sides: $4x-11 + 11=5 + 11$, so $4x=16$. Divide both sides by 4: $x = 4$.

Step4: Find the length of RT

Substitute $x = 4$ into the expression for RT. Since $RT=x + 5$, then $RT=4 + 5=9$.

Answer:

9