Question

1. find the lenght of rq and qp

r •———•———• p
x - 1 3x - 3
q
<———8———>
lenght of rq =
lenght of qp =
show your work

Explanation:

Step1: Set up the equation

From the line segment, we know that \( RQ + QP = RP \). Given \( RQ = x - 1 \), \( QP = 3x - 3 \), and \( RP = 8 \). So the equation is \( (x - 1) + (3x - 3) = 8 \).

Step2: Solve for x

Simplify the left side: \( x - 1 + 3x - 3 = 4x - 4 \). So \( 4x - 4 = 8 \). Add 4 to both sides: \( 4x = 12 \). Divide by 4: \( x = 3 \).

Step3: Find RQ

Substitute \( x = 3 \) into \( RQ = x - 1 \): \( RQ = 3 - 1 = 2 \).

Step4: Find QP

Substitute \( x = 3 \) into \( QP = 3x - 3 \): \( QP = 3(3) - 3 = 9 - 3 = 6 \).

Answer:

Length of \( RQ = 2 \)
Length of \( QP = 6 \)