Question

If ABCD is a parallelogram in which P and Q are the centroids of $\Delta ABD$ and $\Delta BCD$, then, PQ equals:

• A. AQ
• B. AP
• C. BP
• D. DQ

Answer 1

The correct option is B AP

R.E.F image

Centroid of $\Delta$ devised each

median in the ratio $2:1$

$\frac{AP}{PO}=\frac{2}{1}$ $\frac{CQ}{OQ}=\frac{2}{1}...\left(1\right)$

We know that diagonal of $\square$ bisect each other

$AO=OC$

$AP+PO=OQ+QC...\left(2\right)$

$2PQ+PO=OQ+2OQ$

$PO=OQ...\left(3\right)$

Similarly $AP=CQ...\left(4\right)$

$AP=2OP=2OQ=QC$

Now, $OP+OQ=OP+OP$ from eq (3)

$PQ=2OP$

$PQ=AP$