Question

1. r, q, and s are collinear and q is between r and s. work and draw a picture. find the length of rq and qs.

rq = 3x + 8
qs = 2x - 5
rs = 43

Explanation:

Step1: Use segment - addition postulate

Since $R$, $Q$, and $S$ are collinear and $Q$ is between $R$ and $S$, we have $RQ + QS=RS$. Substitute the given expressions: $(3x + 8)+(2x - 5)=43$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+2x + 8 - 5=43$, which simplifies to $5x+3 = 43$.

Step3: Solve for $x$

Subtract 3 from both sides of the equation: $5x+3 - 3=43 - 3$, getting $5x=40$. Then divide both sides by 5: $\frac{5x}{5}=\frac{40}{5}$, so $x = 8$.

Step4: Find the length of $RQ$

Substitute $x = 8$ into the expression for $RQ$: $RQ=3x + 8=3\times8 + 8=24 + 8=32$.

Step5: Find the length of $QS$

Substitute $x = 8$ into the expression for $QS$: $QS=2x - 5=2\times8 - 5=16 - 5=11$.

Answer:

$RQ = 32$, $QS = 11$