Applying the definition of a midpoint of a segment, the lengths are:
RT = 74 units
RS = 37 units
The midpoint is defined as the point that bisects a line segment into two equal halves.
If M is the midpoint of RT, therefore:
RS = ST
RS = 6x + 7
ST = 9x - 8
Substitute
6x + 7 = 9x - 8
6x - 9x = -7 - 8
-3x = -15
x = -15/-3
x = 5
RT = RS + ST [segment addition postulate]
RT = 6x + 7 + 9x - 8 [substitution]
RT = 15x - 1
Plug in the value of x
RT = 15(5) - 1
RT = 74 units
RS = 6x + 7 = 6(5) + 7
RS = 37 units.
Thus, applying the definition of a midpoint of a segment, the lengths are:
RT = 74 units
RS = 37 units
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