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: Point O doesn’t lie on the segment AB .

Answer 1

1.5 cm

Explanation:

In the figure attached,

OA = 12 cm and OB = 9 cm.

Let the mid points of OA and OB are P and Q.

Then we have to find the distance between P and Q.

Since P is the midpoint of OA so OP =
`(12)/(2)` = 6 cm.

and Q is the midpoint of OB so OQ =
`(9)/(2)` = 4.5 cm

Now PQ = OP - OQ

= 6 - 4.5

= 1.5 cm.

Distance between the midpoints of segments OA and OB is 1.5 cm.

Answer 2

Short Answer: 1.5
Givens
OA = 12
OB = 9
O does not lie on AB

Argument
The order that these lines must be in is OBA. O is on your left, B is in the middle and A is on your right.

Mark your distances as follows.
OB = 9
BA = 3

Mark the midpoint of OA = M1
Mark the midpoint of OB = M2

M1 = 12 / 2 = 6 so M1 is 6 units from O
M2 = 9/2 = 4.5

The distance between the two midpoints is 6 - 4.5 = 1.5
Answer M1 - M2 = 1.5 <<<<

Nice problem: Thanks for posting.