Question

point r is on line segment \\(overline{qs}\\). given \\(qs = 2x + 2\\), \\(qr = 3x - 5\\), and \\(rs = 5x - 5\\), determine the numerical length of \\(overline{qr}\\).

Explanation:

Step1: Use segment addition postulate

Since R is on \(\overline{QS}\), we have \(QR + RS = QS\). Substituting the given expressions: \((3x - 5)+(5x - 5)=2x + 2\).

Step2: Simplify and solve for x

Combine like terms: \(8x - 10 = 2x + 2\). Subtract \(2x\) from both sides: \(6x - 10 = 2\). Add 10 to both sides: \(6x = 12\). Divide by 6: \(x = 2\).

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

Substitute \(x = 2\) into \(QR = 3x - 5\): \(QR = 3(2)-5 = 6 - 5 = 1\).

Answer:

1