If in a triangle AB=a,AC=b and D,E are t...

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

A

`(a)/(4)-(b)/(4)`

B

`(a)/(2)-(b)/(2)`

C

`(b)/(4)-(a)/(4)`

D

`(b)/(2)-(a)/(2)`

Verified by Experts

The correct Answer is:

D

We know by fundamental theorem of proportionality that,
`DE=(1)/(2)BC`

In triangle, `BC=b-a`
Hence, `DE=(1)/(2)(b-a)`.

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