If P and Q are the middle points of the ...

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

A

AC

B

`(1)/(2)AC`

C

`(2)/(3)AC`

D

`(3)/(2)AC`

Verified by Experts

The correct Answer is:

D

`AP=AB+BP=AB+(1)/(2)BC=AB+(1)/(2)AD` . . . (i)
`AQ=AD+DQ=AD+(1)/(2)DC=AD+(1)/(2)AB` . . . (ii)

By eqs. (i) and (ii), we get
`AP+AQ=(3)/(2)(AB+AD)`
`=(3)/(2)(AB+BC)=(3)/(2)AC`.

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