if A (2,0), B (p,-2), C (-1,1) and D (3,r) are the vertices of a parallelogram ABCD, calculate the value of pand of r

Question

gorv · Answer

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anonymous · Answer

I dont get it. :/

gorv · Answer

in parallelogram opposite sides are parallel 
so their slope will be equal

gorv · Answer

AB parallel to CD it is property of parallelogram that opposite side are alwys parallel to each other

gorv · Answer

slope of AB=slope of CD

anonymous · Answer

Oh, I get it! Thank you so much!

gorv · Answer

if you get any doubt further ask than after giving it a try

anonymous · Answer

Do I have to solve the equation simultaneously afterwards? Because there are two variables. :/

shubhamsrg · Answer

There is a shorter way.
Note that the mid points of AC and BD coincide.

anonymous · Answer

can you please exlpain further?

shubhamsrg · Answer

What is the mid point of AC ?

anonymous · Answer

(1/2, 1/2)?

shubhamsrg · Answer

Correct.
BD's mid point will have the same co-ordinates. ( Diagonals in a parallelogram bisect each other ).
Just equate BD's mid point with (1/2 ,1/2)  and voila! You'll have  your vales for p and q

anonymous · Answer

I got the answerrr!! THANK YOOOU!

shubhamsrg · Answer

Glad to help ^^

anonymous · Answer

@kfatima10
digonals of parallelogram bisect each other .it means mid-point of AB=midpoint of CD.use this and you will get the answer.if you are satisfied ,GIVE ME MEDAL.