Question

point q is on line segment \\(\overrightarrow{pr}\\). given \\(qr = 3x\\), \\(pq = x + 6\\), and \\(pr = 5x - 4\\), determine the numerical length of \\(\overline{pq}\\).

Explanation:

Step1: Use segment addition postulate

Since Q is on \( \overline{PR} \), \( PQ + QR = PR \). Substitute the given expressions: \( (x + 6) + 3x = 5x - 4 \).

Step2: Simplify and solve for x

Combine like terms: \( 4x + 6 = 5x - 4 \). Subtract \( 4x \) from both sides: \( 6 = x - 4 \). Add 4 to both sides: \( x = 10 \).

Step3: Find length of \( \overline{PQ} \)

Substitute \( x = 10 \) into \( PQ = x + 6 \): \( PQ = 10 + 6 = 16 \).

Answer:

16