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moses638
09.07.2020 •
Mathematics
Points P and Q belong to segment AB . If AB = a, AP = 2PQ = 2QB, find the distance: midpoints between AP QB
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Ответ:
The distace between midpoints of AP and QB is
.
Step-by-step explanation: Points P and Q are between points A and B and the segment AB measures a, then:
AP + PQ + QB = a
According to the question, AP = 2 PQ = 2QB, so:
PQ =![\frac{AP}{2}](/tpl/images/0703/4949/fe56e.png)
QB =![\frac{AP}{2}](/tpl/images/0703/4949/fe56e.png)
Substituing:
AP + 2*(
) = a
2AP = a
AP =![\frac{a}{2}](/tpl/images/0703/4949/cef5a.png)
Since the distance is between midpoints of AP and QB:
2QB = AP
QB =![\frac{AP}{2}](/tpl/images/0703/4949/fe56e.png)
QB =![\frac{a}{2}*\frac{1}{2}](/tpl/images/0703/4949/75c23.png)
QB =![\frac{a}{4}](/tpl/images/0703/4949/27969.png)
MIdpoint is the point that divides the segment in half, so:
Midpoint of AP:
Midpoint of QB:
The distance is:
d =![\frac{a}{4} - \frac{a}{8}](/tpl/images/0703/4949/9f99e.png)
d =![\frac{a}{8}](/tpl/images/0703/4949/10af8.png)
Ответ:
lol no.
Step-by-step explanation: