(A) 3 cm
Explanation:
According to the figure,
ΔQRW, ΔQSV and ΔQTU would be congruent to each other.
S is the mid point of QT
So, QS = ST = 9cm
Similarly, V is the midpoint of QU
So, QV = VU = 6 cm
QV = 6 cm
QW + WV = 6 cm
QW + 4 = 6
QW = 2 cm
Now considering ΔQRW and ΔQSV:
By following the rule of congruence,
[tex]\frac{QR}{RS} = \frac{QW}{WV} \\\\\frac{QR}{9 - QR} = \frac{2}{4} \\\\[/tex]
[tex]\frac{QR}{9 - QR} = \frac{1}{2} \\\\2QR = 9 - QR\\\\3QR = 9\\\\QR = 3cm[/tex]
Thus, the length of segment QR is 3cm
