Answer:
7. VS = 17
8. QR = 6
9. UT = 17
Explanation:
You have trapezoid QRTU with midsegment VS parallel to bases QR and TU. Given dimensions for two of these parallel lines, you want the measure of the third.
Segment relationships
The markings on the parts of segments QU and RT indicate that points V and S are their midpoints, respectively. This makes segment VS a "midsegment", one that joins the midpoints of opposite sides. As such, its length is the average of the lengths of QR and TU:
VS = (QR +TU)/2
This is the relation that is used for problem 7.
For problems 8 and 9, this is rearranged to give the values of QR and UT:
QR = 2VS -UT
UT = 2VS -QR
7. VS
From above, ...
VS = (QR +UT)/2 = (12 +22)/2
VS = 17
8. QR
From above, ...
QR = 2VS -UT = 2(9) -12
QR = 6
9. UT
From above, ...
UT = 2VS -QR = 2(11) -5
UT = 17
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Additional comment
You will note that the line segments form an arithmetic sequence: the difference in length between adjacent segments is the same.
7: 12, 17, 22
8: 6, 9, 12
9: 5, 11, 17