Question

PQ=9y−2 and QR=14+5y. Find the measure of line segment PQ if Q is the midpoint of line segment PR.

a) 9y−16
b) 9y−2
c) 14+5y
d) 5y−16

Answer 1

Since Q is the midpoint of PR, PQ equals QR. By setting 9y - 2 (PQ) equal to 14 + 5y (QR), we solve for y = 4, and find that PQ = 34, which is not listed in the provided options.

Step-by-step explanation:

To answer the question, we must first recognize that since Q is the midpoint of PR, the lengths of PQ and QR must be equal. Therefore, we can set the expressions for PQ and QR equal to each other to find the value of y and then determine the length of PQ:

• PQ = 9y - 2
• QR = 14 + 5y

Since PQ = QR, we have:

9y - 2 = 14 + 5y

Subtracting 5y from both sides:

4y - 2 = 14

Adding 2 to both sides:

4y = 16

Dividing by 4:

y = 4

We can now plug this value back into the expression for PQ:

PQ = 9(4) - 2

PQ = 36 - 2

PQ = 34

The measure of line segment PQ is 34, which isn't one of the listed options, indicating a possible typo in the provided choices.