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

10.5 cm

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}`

Answer 2

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.