Question

Points o, a, b lie on the same line. oa = 12 cm, ob = 9 cm. find the distance between the midpoints of segments oa and ob if: a point o lies on the segment ab

Answer 1

If the order of points is A, O, B, then the midpoints of AO and OB will be separated by half the length of AB: (12 cm + 9 cm)/2 = 10.5 cm.

Answer 2

Answer:

10.5 cm

Step-by-step explanation:

Given: Points $\text{o}$,$\text{a}$ and $\text{b}$ lie on the same line. $\text{oa}$ $=12\text{cm}$, $\text{ob}$  $=8\text{cm}$, point $\text{o}$ lies on the segment $\text{ab}$.

To Find: find the distance between the midpoints of segments oa and ob.

Solution:

point $\text{o}$ lies on the segment $\text{ab}$

Therefore,

          $\text{ab}=\text{oa}+\text{ob}$

distance of midpoint of $\text{oa}$ from $\text{o}$

                                   $\frac{\text{oa}}{2}$

                                   $6\text{cm}$

distance of midpoint of $\text{ob}$ from $\text{o}$

                                   $\frac{\text{ob}}{2}$

                                   $4.5\text{cm}$

Distance between midpoints of  $\text{oa}$ and $\text{ob}$

                                   $=\frac{\text{oa}}{2}+\frac{\text{ob}}{2}$

putting values

                                   $=6+4.5$

                                   $=10.5$ $\text{cm}$

Hence distance between midpoints of line segments $\text{oa}$ and $\text{ob}$ is  $=10.5$ $\text{cm}$