Question

HELP QUICKKKKK:Point B lies on the segment AC whose length AC = a cm. Find the distance between the midpoints of segments AB and BC .

Answer 1

Answer with Step-by-step explanation:

We are given that point B lies on the segment AC.

Length of AC= a cm

We have to find the the distance between the midpoint of segment AB and BC.

When B lies on the segment AC.

Let mid point of segment AB and BC are E and F.

E is the midpoint of segment AB.

Therefore, $AE=EB$

$BF=FC$

$AC=AE+EB+BF+FC=EB+EB+BF+BF$

$a=2EB+2BF$

$2(EB+BF)=a$

$EB+BF=\frac{a}{2}$

Distance between E and F is given by

$EF=EB+BF$

$EF=\frac{a}{2} cm$

Hence, the distance between the midpoints of segment AB and BC is given by

$EF=\frac{a}{2} cm$