Based on the diagram, the length of segment QS is 17 units.
In Mathematics and Geometry, a perpendicular bisector is a segment, or ray that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
Based on the definition of a perpendicular bisector, we can logically deduce the following congruent sides;
RT = TQ
RS = QS
3x + 2 = 5x - 8
5x - 3x = 2 + 8
2x = 10
x = 10/2
x = 5 units.
Now, we can determine the length of segment QS as follows;
QS = 5x - 8
QS = 5(5) - 8
QS = 25 - 8
QS = 17 units.
Complete Question:
Consider the diagram.
The length of segment QS__ is units.