Question

directions: suppose q is the midpoint of pr. use the information to find the missing value

1. ( p q = 3 x + 14 ) and ( q r = 7 x - 10 ). find x.
2. ( p q = 2 x + 1 ) and ( q r = 5 x - 44 ). find pq
3. ( p q = 6 x + 25 ) and ( q r = 16 - 3 x ). find pr.
4. ( p r = 9 x - 31 ) and ( q r = 43 ). find x.

Explanation:

Step1: Use midpoint property

Since \(Q\) is the midpoint of \(PR\), \(PQ = QR\). So, \(3x + 14=7x - 10\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(14 = 4x-10\).
Add \(10\) to both sides: \(24 = 4x\).
Divide both sides by \(4\): \(x = 6\).

Answer:

\(x = 6\)