Answer:
The distance between midpoint of AP and QB is [tex]\frac{5a}{8}[/tex].
Step-by-step explanation:
Given that: AB = a
AP = 2PQ = 2QB
Thus,
PQ = QB = [tex]\frac{a}{4}[/tex]
PQ + QB = [tex]\frac{a}{4}[/tex]+ [tex]\frac{a}{4}[/tex]
= [tex]\frac{a}{2}[/tex]
AP = [tex]\frac{1}{2}[/tex] a = [tex]\frac{a}{2}[/tex]
The distance between midpoint of AP and QB can be determined as;
[tex]\frac{AP}{2}[/tex] + PQ + [tex]\frac{QB}{2}[/tex]
= [tex]\frac{a}{4}[/tex] + [tex]\frac{a}{4}[/tex] + [tex]\frac{a}{8}[/tex]
= [tex]\frac{2a+2a+a}{8}[/tex]
= [tex]\frac{5a}{8}[/tex]
Therefore, the distance between midpoint of AP and QB is [tex]\frac{5a}{8}[/tex].
