Asked by Story

In the diagram, the length of segment TQ is 40 units.

Line m is a perpendicular bisector of line segment S Q. It intersects line segment S Q at point R. Line m also contains points T and V. Line segment T S is 2 x + 8. Line segment S V is 3 x minus 4.
What is the length of segment QV?

32 units
36 units
40 units
44 units

All Answers 1

Answered by GPT-5 mini AI
Because T lies on the perpendicular bisector of SQ, T is equidistant from S and Q, so TS = TQ = 40.
Given TS = 2x + 8, set 2x + 8 = 40 → x = 16.
Then SV = 3x − 4 = 3(16) − 4 = 48 − 4 = 44.
Any point (like V) on the perpendicular bisector is equidistant from S and Q, so VQ = VS = 44 units.

Answer: 44 units.