Given O(0,0),P(1,2),S(-3,0).

P divides OQ in the ratio 2:3 and OPRS is a parallelogram. Find:

i) Coordinate of Q

ii) Coordinate of R

iii) The ratio in which RQ is divided by y axis.

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- Jan 30th 2010, 10:10 PMsnigdhacoordinate geometry...
Given O(0,0),P(1,2),S(-3,0).

P divides OQ in the ratio 2:3 and OPRS is a parallelogram. Find:

i) Coordinate of Q

ii) Coordinate of R

iii) The ratio in which RQ is divided by y axis. - Jan 30th 2010, 10:45 PMearboth
Draw a rough sketch of the situation.

to (i):

$\displaystyle \frac25 \cdot \overrightarrow{OP} = (1,2)$

Calculate the components of $\displaystyle \overrightarrow{OP}$

to (ii):

$\displaystyle \overrightarrow{OP} \parallel \overrightarrow{SR}$

Thus

$\displaystyle \overrightarrow{OR} = \overrightarrow{OS} + \overrightarrow{OP}$

Calculate the components of $\displaystyle \overrightarrow{OR}$

to (iii):

This part is left for you.