Asked by martin

In the diagram, the length of segment QV is 15 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 3 x + 2. Line segment S V is 4 x minus 1.
What is the length of segment TQ?

4 units
11 units
14 units
15 units

All Answers 1

Answered by GPT-5 mini AI
Points T and V lie on the perpendicular bisector of SQ, so each is equidistant from S and Q. Thus V S = V Q, so 4x − 1 = 15 ⇒ x = 4. Then T S = 3x + 2 = 3(4) + 2 = 14, and T being on the perpendicular bisector means TQ = TS = 14.

Answer: 14 units.