P, Q, and R are three collinear points that exist such that segment PQ and segment QR are congruent. PQ= 6x-8
and QR= 10x-44
How long is segment PR
Answer
Final Answer: The length of segment PR is \(\boxed{92}\).
Step 1 ：Given that P, Q, and R are three collinear points and segment PQ and segment QR are congruent, we have PQ = QR.
Step 2 ：Given that PQ = 6x - 8 and QR = 10x - 44, we can set these two expressions equal to each other to solve for x: \(6x - 8 = 10x - 44\).
Step 3 ：Solving the equation gives us the value of x as \(x = 9\).
Step 4 ：Substituting x = 9 back into either the expression for PQ or QR, we find that PQ = QR = 46.
Step 5 ：Since PR is the sum of PQ and QR, and PQ = QR, we can simply multiply the length of PQ or QR by 2 to find the length of PR: \(PR = 2 * PQ = 2 * 46 = 92\).
Step 6 ：Final Answer: The length of segment PR is \(\boxed{92}\).
