Question

Line RS bisects segment PQ at R. If RQ = x + 9 and RP = 2x, find PQ.

Answer 1

PQ measures 36 units.

Explanation:

Line RS bisects segment PQ at R. By the definition of a bisector:

`\displaystyle PR = RQ`

Hence:

We are given that RQ = x + 9 and RP = 2x, and we want to determine PQ.

Solve for x. Substitute:

`\displaystyle (2x) = (x+9)`

Hence:

`\displaystyle x = 9`

PQ is given by:

`\displaystyle PQ = PR + RQ`

Since PR = RQ:

`\displaystyle PQ =2PR`

Substitute and evaluate:

`\displaystyle \begin{aligned} PQ &= 2PR \\ &= 2(2x) \\ &= 4x \\ &= 4(9) \\ &= 36 \end{aligned}`

Hence, PQ measures 36 units.