Question

Determine the measure of Segment PQ, if Q is the midpoint of Segment PR, and PQ = 9y -2 and QR = 14 + 5y.

Answer 1

We have the segments PQ and PR, with the following information:

- Q is the midpoint of PR.

- PQ = 9y-2

- QR = 14+5y

We can draw this as:

As Q is the midpoint, both PQ and QR are equal, so we can write this and solve for y:

$\begin{gathered} PQ=QR \\ 9y-2=14+5y \\ 9y-5y=14+2 \\ 4y=16 \\ y=\frac{16}{4} \\ y=4 \end{gathered}$

Then, the measure of PQ is:

$PQ=9y-2=9\cdot4-2=36-2=34$

The measure of PQ is 34.