Question

1. point t is the midpoint of segment rs. if rt = 5x - 2 and ts = 3x + 4, what is the length of rs?

a) 6
b) 26
c) 14
d) 2
○ a) 6
○ b) 26
○ c) 14
○ d) 2

Explanation:

Step1: Set RT equal to TS

Since T is the mid - point of RS, RT = TS. So, $5x - 2=3x + 4$.

Step2: Solve for x

Subtract 3x from both sides: $5x-3x - 2=3x-3x + 4$, which simplifies to $2x-2 = 4$. Then add 2 to both sides: $2x-2 + 2=4 + 2$, giving $2x=6$. Divide both sides by 2: $x = 3$.

Step3: Find the length of RT or TS

Substitute x = 3 into the expression for RT. RT=$5x - 2=5\times3-2=15 - 2=13$. (We could also use the expression for TS: TS=$3x + 4=3\times3+4=9 + 4 = 13$).

Step4: Find the length of RS

Since RS=RT + TS and RT = TS = 13, then RS=13 + 13=26.

Answer:

B. 26