Question

segment tq is 26 units long. what is the length of qv? 8 units 26 units 31 units 32 units

Explanation:

Step1: Find the value of \(x\)

Since \(SR\) is the perpendicular bisector of \(TV\), \(ST = SV\). So, \(3x + 2=4x - 1\).
Subtract \(3x\) from both sides: \(2=x - 1\).
Add \(1\) to both sides: \(x = 3\).

Step2: Find the length of \(SV\)

Substitute \(x = 3\) into \(4x-1\): \(4\times3-1=12 - 1=11\).

Step3: Use the property of perpendicular bisector

Since \(SR\) is the perpendicular bisector of \(TV\), \(TQ = VQ\) (by the property that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment). Given \(TQ = 26\), so \(VQ=26\).

Answer:

\(26\) units