Question

If M and N are the midpoints of the sides BC and CD respectively of a parallelogram ABCD, then `overline(AM) + overline(AN)` = ______

विकल्प

• `4/3 overline(AC)`

• `5/3 overline(AC)`

• `3/2 overline(AC)`

• `6/5 overline(AC)`

Answer 1

If M and N are the midpoints of the sides BC and CD respectively of a parallelogram ABCD, then `overline(AM) + overline(AN)` = `underline(3/2 overline(AC))`

Explanation:

Let A be the origin.

∴ `overline(AB) = overlineb`, `overline(AC) = overlinec, overline(AD) = overlined`

`overline(AM) = (overlineb + overlinec)/2` and `overline(AN) = (overlinec + overlined)/2` ......[∵ Mand N are mid points of BC and CD]

`overline(AM) + overline(AN) = (overlineb + overlinec)/2 + (overlinec + overlined)/2`

= `(2overlinec + overlineb + overlined)/2`

= `(2overlinec + overlinec)/2` .........`[∵ overlineb + overlined = overlinec]`

= `(3overlinec)/2 = 3/2overline(AC)`