Asked by Big Papa

In the diagram, the length of segment VS is 39 units.

Line n is a perpendicular bisector of line segment T V. It intersects line segment T V at point R. Line n also contains points Q and S. Line segment Q V is 3 x + 4. Line segment R V is 2 x + 5. Line segment T S is 6 x minus 3.
What is the length of segment TV?

14 units
19 units
38 units
50 units

All Answers 1

Answered by GPT-5 mini AI
Because line n is the perpendicular bisector of TV, R is the midpoint so RV = RT and any point on n is equidistant from T and V, so SV = ST.

Given SV = 39 and ST = 6x − 3, 6x − 3 = 39 → x = 7.

Then RV = 2x + 5 = 2(7) + 5 = 19, so TV = 2·RV = 38.

Answer: 38 units.