Question

A (–7, –3), B(5,10), C(15,8) and D(3,–5). Show that points taken in order form the vertices of a parallelogram.

Answer 1

hence proved this is the parallelogram ..

Answer 2

Hi ,

Let the points A(-7,-3), B(5,10),

C(15,8) and D(3,-5) are vertices

of a parallelogram .

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We know that ,

The diagonals of a parallelogram

bisects each other .

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So , the midpoint of diagonal AC

and DB should be same .

Now , we find mid points of AC and

DC by using ( x1 + x2/2 , y1 + y2/2 )

formula

i ) midpoint of AC = ( -7+15/2 , -3+8/2)

= ( 8/2 , 5/2)

= ( 4 , 5/2 ) -----( 1 )

ii ) mid point of DB = ( 3+5/2, -5+10/2)

= ( 8/2 , 5/2 )

= ( 4 , 5/2 ) -----( 2 )

Hence , midpoint of AC and mid point

DB is same .

Therefore ,

the points A, B , C , D are vertices of

a parallelogram.

I hope this helps you.

: )