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Flura [38]
2 years ago
5

Segment AB has length a and is divided by points P and Q into AP , PQ , and QB , such that AP = 2PQ = 2QB. A) Find the distance

between point A and the midpoint of segment QB . B) Find the distance between the midpoints of segments AP and QB .
Mathematics
1 answer:
Deffense [45]2 years ago
7 0

Answer:

A) \frac{7}{8}a

B) \frac{5}{8}a

Step-by-step explanation:

AB has length a and is divided by points P and Q into AP , PQ , and QB , such that AP = 2PQ = 2QB

A) Therefore, AP = 2QB

QB = AP/2

The midpoint of QB = QB/2 = (AP/2)/2 = AP/4

AP = 2PQ, Therefore PQ = AP/2

Since the length of AB = a

AB = AP + PQ + QB = a

AP + AP/2 + AP/2 = a

AP + AP = a

2AP = a

AP = a/2

The distance between point A and the midpoint of segment QB = AP + PQ + QB/2 = AP + AP/2 + AP/4 = 7/4(AP)

But AP = a/2

Therefore The distance between point A and the midpoint of segment QB =  7/4(a/2)= \frac{7}{8}a

B)

the distance between the midpoints of segments AP and QB = AP/2 + PQ + QB/2 = AP/2 + AP/2 + AP/4 = 5/4(AP)

But AP = a/2

Therefore the distance between the midpoints of segments AP and QB = 5/4(AP) = \frac{5}{4} *\frac{a}{2}=\frac{5}{8}a

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-------------------------------

DISCLAIMER: I am not a professional tutor or have any professional background in your subject. Please do not copy my work down, as that will only make things harder for you in the long run. Take the time to really understand this, and it'll make future problems easier. I am human, and may make mistakes, despite my best efforts. Again, I possess no professional background in your subject, so anything you do with my help will be your responsibility. Thank you for reading this, and have a wonderful day/night!
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