Question

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 R V is 3 x + 2. Line segment Q V is 4 x + 1. Line segment T S is 9 x minus 4.
The length of TR is 17 units. What are the lengths of SV and QT?

SV =
units

QT =
units

Answer 1

Since R is the midpoint of TV, RV = TR = 17. So 3x + 2 = 17 → x = 5.

QV = 4x + 1 = 4(5) + 1 = 21. Point Q lies on the perpendicular bisector, so QT = QV = 21.

TS = 9x − 4 = 9(5) − 4 = 41. Point S lies on the perpendicular bisector, so SV = ST = 41.

SV = 41 units
QT = 21 units