Question

in the diagram, the length of segment tq is 40 units. what is the length of segment qv? 32 units 36 units 40 units 44 units

Explanation:

Step1: Find the value of \(x\)

Since \(ST = SQ\) (by the property of perpendicular bisector), we have \(2x + 8=3x - 4\).

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Step2: Find the length of \(SV\)

Substitute \(x = 12\) into \(3x - 4\), \(SV=3\times12-4=36 - 4=32\).

Step3: Prove \(TQ = QV\)

Because line \(m\) is the perpendicular bisector of \(SQ\), so \(TQ = QV\) (by the property of perpendicular bisector: any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment). Given \(TQ = 40\) units, so \(QV = 40\) units.

Answer:

40 units