Final answer:
To find the values of x, PQ, QR, and PR, we can set the expressions for PR and QR equal to each other and solve for x. Substituting the value of x into the expressions for PQ, QR, and PR gives us the respective values. Therefore, x = 4/17, PQ = 90/17, QR = 78/17, and PR = 90/17.
Step-by-step explanation:
A) To find x, we can set the expressions for PR and QR equal to each other since Q is the midpoint of PR.
PR = QR
14x + 2 = 6 - 3x
Solving for x:
14x + 3x = 6 - 2
17x = 4
x = 4/17
B) To find PQ, we can substitute the value of x into the expression for PQ.
PQ = 14(x) + 2
= 14(4/17) + 2
= 90/17
C) To find QR, we can substitute the value of x into the expression for QR.
QR = 6 - 3(x)
= 6 - 3(4/17)
= 78/17
D) To find PR, we can substitute the value of x into the expression for PR.
PR = 14(x) + 2
= 14(4/17) + 2
= 90/17